Word Problems

Distance, Speed, Time

3. Shantiel left her home at 9:00 a.m. on Tuesday and traveled 648 miles. When she arrived at her destination it was 3:00 a.m. the next day. Given that her home and her destination are in the same time zone, which of the following is closest to her average speed, in miles per hour, for this trip?

2018 June(A11) Math Question 3

2019 April(B04) Math Question 6

8. Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.

2017 June(74C) Math Question 8

2010 April(68G) Math Question 8

8. Manish drove from Chicago to Baton Rouge. At 8:00 a.m., he was 510 km from Baton Rouge. At 1:00 p.m., he was 105 km from Baton Rouge. Which of the following values is closest to Manish’s average speed, in kilometers per hour, from 8:00 a.m. to 1:00 p.m. ?

Speed, Distance, and Time

2021 April(Z04) Math Question 8

2019 April(Z15) Math Question 8

2012 April(70G) Math Question 9

9. Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at 1-second intervals from t = 0 seconds to t= 5 seconds.

2014 June(72C) Math Question 9

11. Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.

2014 December(72G) Math Question 11

11. The speed of one motorcycle exceeds 4 times the speed of another motorcycle by 24 mph. The speed of the slower motorcycle is g mph. Which of the following expressions represents the speed of the faster motorcycle, in miles per hour?

2015 December(72E) Math Question 11

2011 June(69F) Math Question 12

12. Tim’s flight was originally scheduled to depart at 4:51 p.m., but it was delayed 563 minutes. What time did Tim’s flight eventually depart?

2021 June(D06) Math Question 12

12. In Cherokee County, the fine for speeding is $17 for each mile per hour the driver is traveling over the posted speed limit. In Cherokee County, Kirk was fined $221 for speeding on a road with.a posted speed limit of 30 mph. Kirk was fined for traveling at what speed, in miles per hour?

2017 April(74F) Math Question 12

13. Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.

2015 December(72E) Math Question 13

14. Rajeev went on a delivery trip that began and ended at his truck terminal. He used all of the time during the trip driving, unloading, or resting. Rajeev began his trip on Tuesday at 7:00 a.m. when he left the terminal. During his driving time, he drove 1,200 miles at an average speed of 50 miles per hour. His driving time was twice as long as his unloading time, and his resting time was 30 hours. When did Rajeev end his delivery trip?

2015 December(72E) Math Question 14

17. A car accelerated from 88 feet per second (fps) to 220 fps in exactly 3 seconds. Assuming the acceleration was constant, what was the car's acceleration, in feet per second per second, from 88 fps to 220 fps ?

2014 June(72C) Math Question 17

2020 July(C01) Math Question 20

20. You drove 18 miles in 20 minutes at a constant speed and did NOT exceed the speed limit, given in miles per hour. Among the following, which is the lowest that the speed limit could have been?

2021 December(E23) Math Question 20

22. A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assuming the truck continues at 35 mph and its radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty?

2018 April(A09) Math Question 22

2012 December(71A) Math Question 27

27. A pedometer records the number of steps a person takes as he or she walks. When a pedometer records 3,898 steps taken by a person who covers a distance of 2.25 feet per step, how much distance, to the nearest 0.1 mile, did the person cover? (Note: 1 mile = 5,280 feet)

Unit Conversions (Feet to inches, miles to feet, hours to seconds)

2021 December(E23) Math Question 27

2019 April(Z15) Math Question 28

28. A full lap is 2 times the length of the pool. Johann swam 5 full laps of the pool in 44- minutes. Which of the following values is closest to Johann’s average swimming speed, in feet per minute?

2018 June(A11) Math Question 28

2009 April(66F) Math Question 31

32. You and a friend each have a can full of water. You start pouring the water from your can into an empty bucket at a constant rate of 4 ounces per second. While you are still pouring water, 3 seconds after you started, your friend starts pouring the water from her can into the same bucket at a constant rate of 2 ounces per second. How many seconds after you first started pouring the water into the bucket will it contain 24 ounces of water?

2021 June(D06) Math Question 32

33. Use the following information to answer questions 33–36. Fletcher purchased 5 items at Hippity-Bippity Toy Store for a total of $18.55, which included sales tax. When he arrived home, he discovered that his receipt was torn and did not show the price of the bag of balloons or the 6% sales tax applied to the sum of the 5 prices. The partial receipt is shown below.Fletcher left his home 1 hour  15 minutes before he entered the store. He spent 25 minutes in the store before he made his purchase. What time did Fletcher leave his home?

Elapsed time

2021 December(E23) Math Question 33

2018 December(B05) Math Question 35

38. Walter recently vacationed in Paris. While there, he visited the Louvre, a famous art museum. Afterward, he took a 3.7-kilometer cab ride from the Louvre to the Eiffel Tower. A tour guide named Amelie informed him that 2.5 million rivets were used to build the tower, which stands 320 meters tall. 38. Walter’s cab ride lasted 15 minutes. Which of the following values is closest to the average speed, in miles per hour, of the cab? (Note: 1 mile 1.6 kilometers)

2018 June(A11) Math Question 38

40. A certain robin flew for 15 seconds at the maximum reported flight speed cited by the website. Which of the following values is closest to the number of meters the robin flew during that time? (Note: 1 meter ≈ 3.3 feet)

2020 December(D03) Math Question 40

41. Use the following information to answer questions 41–43. The table below is part of a delivery truck log used in Aaron’s trucking business. “Mileage out” and “Mileage in” represent the truck’s mileage readings when it leaves the office and when it returns to the office, respectively, giving only the last 3 digits of the cumulative mileage reading. The “Hours away” column gives the amount of time from when the truck leaves the office until it returns to the office. When moving, the truck travels at an average speed of 50 miles per hour and does not travel more than 1,000 miles in any given day. Driver Ben forgot to complete the log for June 18. 41. According to the mileage reading, what distance, in miles, did the truck travel on June 20 ?

Algebraic Problems

2021 April(D05) Math Question 41

42. Emma and Kristin each ran 10 laps (4,000 meters) around a 400-meter track without stopping. Emma ran at a constant speed of 250 meters per minute. Kristin ran at a constant speed of 200 meters per minute. Both Emma and Kristin began running at the same instant. How many laps did Kristin have left to run when Emma had completed her run?

2014 December(72G) Math Question 42

42. The figure shown below represents the route traveled on July 16. Aaron started at the office, drove 75 miles due north to the 1st stop, then 40 miles due east to the 2nd stop, and then 105 miles due south to the last stop. On his return trip, Aaron drove a straight road from the last stop to the office without stopping. Given that Aaron drove at the truck’s average speed, which of the following values is closest to the time, in hours, Aaron drove on the return trip?

Pythagorean Theorem and Special Right Triangles

2021 April(D05) Math Question 42

43. Juro traveled to 3 locations during a workday. Juro remained at each location a whole number of hours. The graph below shows the relationship between time, in hours, into his workday and total distance, in kilometers, traveled. Which of the following values is closest to Juro’s average speed, in kilometers per hour, for the parts of the workday when he was traveling?

2021 December(E23) Math Question 43

2020 July(C01) Math Question 44

2019 December(C03) Math Question 45

2012 December(71A) Math Question 46

52. Jarrod went on Tour A, and his trip. covered a distance
of 6 miles. Bhumi went on Tour C, and her trip covered
a distance of 9 miles. Which of the following values is
the difference, in miles per hour, of the average speeds
of their balloons during their tours?

2019 June(B02) Math Question 52

53. It took 0.5 second for an object to travel 60.5 feet. To the nearest 0.01 mile per hour, what was the speed of the object? (Note: 1 mile = 5,280 feet)

2021 April(D05) Math Question 53

54. Vanna walked at a rate of 2 miles per hour for 10 minutes and then walked at a rate of 3 miles per hour for 5 minutes. Which of the following gives the average rate, in miles per hour, at which she walked over this 15-minute period?

2018 June(A11) Math Question 54

55. Carrie and Manuel are side by side when they begin to run at the same time in the same direction around a track. Carrie runs at a constant rate of 30 seconds per lap, while Manuel runs at a constant rate of 50 seconds per lap. How many seconds after beginning to run will Carrie have run exactly 1 more lap than Manuel?

2016 April(73E) Math Question 55

2020 July(C01) Math Question 55

60. Lucinda ran a 3-mile cross-country course in 24.0 minutes while Frannie ran the same course in 21.0 minutes. Which of the following values, in miles per hour, is closest to the difference between Frannie’s average speed and Lucinda’s average

Distance, Speed, TimeWord ProblemsACT math questions

2018 June(A11) Math Question 3

2019 April(B04) Math Question 6