How to find rate - PSAT Math
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A family is on a road trip from Cleveland to Virginia Beach, totaling 600 miles. If the first half of the trip is completed in 6.5 hours and the second half of the trip is completed in 5.5 hours, what is the average speed in miles per hour of the whole trip?
A family is on a road trip from Cleveland to Virginia Beach, totaling 600 miles. If the first half of the trip is completed in 6.5 hours and the second half of the trip is completed in 5.5 hours, what is the average speed in miles per hour of the whole trip?
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Take the total distance travelled (600 miles) and divide it by the total time travelled (6.5 hrs + 5.5 hrs = 12 hours) = 50 miles/hour
Take the total distance travelled (600 miles) and divide it by the total time travelled (6.5 hrs + 5.5 hrs = 12 hours) = 50 miles/hour
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Two electric cars begin moving on circular tracks at exactly 1:00pm. If the first car takes 30 minutes to complete a loop and the second car takes 40 minutes, what is the next time they will both be at the starting point?
Two electric cars begin moving on circular tracks at exactly 1:00pm. If the first car takes 30 minutes to complete a loop and the second car takes 40 minutes, what is the next time they will both be at the starting point?
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Call the cars “Car A” and “Car B”.
The least common multiple for the travel time of Car A and Car B is 120. We get the LCM by factoring. Car A’s travel time gives us 3 * 2 * 5; Car B’s time gives us 2 * 2 * 2 * 5. The smallest number that accommodates all factors of both travel times is 2 * 2 * 2 * 3 * 5, or 120. There are 60 minutes in an hour, so 120 minutes equals two hours. Two hours after 1:00pm is 3:00pm.
Call the cars “Car A” and “Car B”.
The least common multiple for the travel time of Car A and Car B is 120. We get the LCM by factoring. Car A’s travel time gives us 3 * 2 * 5; Car B’s time gives us 2 * 2 * 2 * 5. The smallest number that accommodates all factors of both travel times is 2 * 2 * 2 * 3 * 5, or 120. There are 60 minutes in an hour, so 120 minutes equals two hours. Two hours after 1:00pm is 3:00pm.
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If Jon is driving his car at ten feet per second, how many feet does he travel in 30 minutes?
If Jon is driving his car at ten feet per second, how many feet does he travel in 30 minutes?
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If Jon is driving at 10 feet per second he covers 10 * 60 feet in one minute (600 ft/min). In order to determine how far he travels in thirty minutes we must multiply 10 * 60 * 30 feet in 30 minutes.
If Jon is driving at 10 feet per second he covers 10 * 60 feet in one minute (600 ft/min). In order to determine how far he travels in thirty minutes we must multiply 10 * 60 * 30 feet in 30 minutes.
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An arrow is launched at 10 meters per second. If the arrow flies at a constant velocity for an hour, how far has the arrow gone?
An arrow is launched at 10 meters per second. If the arrow flies at a constant velocity for an hour, how far has the arrow gone?
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There are 60 seconds in a minute and 60 minutes in an hour, therefore 3600 seconds in an hour. The arrow will travel 3600x10= 36,000 meters in an hour.
There are 60 seconds in a minute and 60 minutes in an hour, therefore 3600 seconds in an hour. The arrow will travel 3600x10= 36,000 meters in an hour.
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If Jack ran at an average rate of 7 miles per hour for a 21 mile course, and Sam ran half as fast for the same distance, how much longer did it take for Sam to run the course than Jack?
If Jack ran at an average rate of 7 miles per hour for a 21 mile course, and Sam ran half as fast for the same distance, how much longer did it take for Sam to run the course than Jack?
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Using the rate formula: Distance = Rate x Time,
Since Jack’s speed was 7 mph, Jack completed the course in 3 hours
21 = 7 x t
t = 3
Sam’s speed was half of Jack’s speed: 7/2 = 3.5
21 = 3.5 x t
t = 6
Therefore it took Sam 3 hours longer to run the course.
Using the rate formula: Distance = Rate x Time,
Since Jack’s speed was 7 mph, Jack completed the course in 3 hours
21 = 7 x t
t = 3
Sam’s speed was half of Jack’s speed: 7/2 = 3.5
21 = 3.5 x t
t = 6
Therefore it took Sam 3 hours longer to run the course.
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If a pail collects x ounces of dripping water every 15 minutes, how many ounces will it collect in h hours?
If a pail collects x ounces of dripping water every 15 minutes, how many ounces will it collect in h hours?
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Algebraic solution: First, convert minutes to hours.
60/15 = 4, so there are 4 15-minute increments in each hour. Therefore, 4x ounces of water are collected each hour. Multiply by h to get 4xh as the solution
Plug-in method: Just choose numbers.
x = 2
h = 3
If 2 ounces drip in 15 minutes, how many ounces will drip in one hour?
2/15 = x/60
15x = 120
x = 8
If 8 ounces drip in one hour, how many ounces will drip in 3 hours? (remember we chose that h = 3)
3 x 8 = 24
This is the answer we are looking for.
Plug x = 2, and h = 3 into each answer choice, to determine which will work. Remember you must plug into every answer choice in case more than one works. In that case, choose different values for x and h, and plug into only the choices that worked the first time.
Algebraic solution: First, convert minutes to hours.
60/15 = 4, so there are 4 15-minute increments in each hour. Therefore, 4x ounces of water are collected each hour. Multiply by h to get 4xh as the solution
Plug-in method: Just choose numbers.
x = 2
h = 3
If 2 ounces drip in 15 minutes, how many ounces will drip in one hour?
2/15 = x/60
15x = 120
x = 8
If 8 ounces drip in one hour, how many ounces will drip in 3 hours? (remember we chose that h = 3)
3 x 8 = 24
This is the answer we are looking for.
Plug x = 2, and h = 3 into each answer choice, to determine which will work. Remember you must plug into every answer choice in case more than one works. In that case, choose different values for x and h, and plug into only the choices that worked the first time.
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Mary can make 20 snowballs in an hour. Mark can make 15 snowballs in 30 minutes. If they work together, how long will it take them to make 150 snowballs?
Mary can make 20 snowballs in an hour. Mark can make 15 snowballs in 30 minutes. If they work together, how long will it take them to make 150 snowballs?
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If Mark makes 15 snowballs in 30 minutes, he can make 30 snowballs in an hour. Working together they can 50 snowballs in one hour. 150 snowballs divided by the amount they can make in one hour (50) will give us the total time it will take them to make 150 snowballs. In this case, 3 hours.
If Mark makes 15 snowballs in 30 minutes, he can make 30 snowballs in an hour. Working together they can 50 snowballs in one hour. 150 snowballs divided by the amount they can make in one hour (50) will give us the total time it will take them to make 150 snowballs. In this case, 3 hours.
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Car X used 4 gallons of gas in one week, and gets 10 miles to the gallon. If car Y went the same number of miles but only gets 8 miles to the gallon, how much gas did car Y use?
Car X used 4 gallons of gas in one week, and gets 10 miles to the gallon. If car Y went the same number of miles but only gets 8 miles to the gallon, how much gas did car Y use?
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We first use the data for car X to conclude that car X went 40 miles (4gallons*10mi/gallon). We then use 40 miles for car Y, and divide 40 by 8, to give us 5 gallons of gas.
We first use the data for car X to conclude that car X went 40 miles (4gallons*10mi/gallon). We then use 40 miles for car Y, and divide 40 by 8, to give us 5 gallons of gas.
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Bob and Sally are doing chores. It takes them 10 hours to do one of their chores. Assuming everyone works at the same rate, how many of their friends would they need to get to help them to do their chores in 2 hours?
Bob and Sally are doing chores. It takes them 10 hours to do one of their chores. Assuming everyone works at the same rate, how many of their friends would they need to get to help them to do their chores in 2 hours?
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Since the kids are trying to do their chores in one fifth of the time, they need five times as many people. Since they have two, five times as many would be ten. We subtract the two of them and that would mean they need 8 more people, giving us answer 8.
Since the kids are trying to do their chores in one fifth of the time, they need five times as many people. Since they have two, five times as many would be ten. We subtract the two of them and that would mean they need 8 more people, giving us answer 8.
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A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
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1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
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Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
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15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
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If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
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Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
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If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
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1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
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If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
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The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
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If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
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Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
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Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
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First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
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The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
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We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
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Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
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Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
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If Kara drives a distance of m miles every h hours, how many hours will it take her to drive a distance of d miles, in terms of m, h, and d ?
If Kara drives a distance of m miles every h hours, how many hours will it take her to drive a distance of d miles, in terms of m, h, and d ?
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We need to convert d miles into hours. We do so by multiplying d miles by the conversion ratio of miles to hours given in the problem, (h hours / m miles), as follows:
d miles * (h hours / m miles) = (dh )/m hours.
From this conversion of miles into hours, we see that the number of hours it takes Kara to drive a distance of d miles is (dh )/m.
We need to convert d miles into hours. We do so by multiplying d miles by the conversion ratio of miles to hours given in the problem, (h hours / m miles), as follows:
d miles * (h hours / m miles) = (dh )/m hours.
From this conversion of miles into hours, we see that the number of hours it takes Kara to drive a distance of d miles is (dh )/m.
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Ruby drives to her grandmother's house and back. On the way there, she travels at an average speed of 40 miles per hour. On the way back, she travels at an average speed of 60 miles per hour. What is Ruby's average speed for the entire round trip?
Ruby drives to her grandmother's house and back. On the way there, she travels at an average speed of 40 miles per hour. On the way back, she travels at an average speed of 60 miles per hour. What is Ruby's average speed for the entire round trip?
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Remember d=rt where d = distance, r = rate, and t = time. In this case, the distance to and the distance from are the same, so we know that
d = _r_1 _t_1 and d = _r_2 _t_2
Since _r_1 = 40 and _r_2 = 60, we can solve for the times and get
_t_1 = d/40 and _t_2 = d/60
Average speed is found by total distance over total time, so we get
Multiplying the numerator and denominator by 120/d we get 240/(3 + 2) = 48.
Remember d=rt where d = distance, r = rate, and t = time. In this case, the distance to and the distance from are the same, so we know that
d = _r_1 _t_1 and d = _r_2 _t_2
Since _r_1 = 40 and _r_2 = 60, we can solve for the times and get
_t_1 = d/40 and _t_2 = d/60
Average speed is found by total distance over total time, so we get
Multiplying the numerator and denominator by 120/d we get 240/(3 + 2) = 48.
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