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Distance, Speed, and Time Word Problems Quiz

Practice 10 distance, speed, and time word problems involving constant speed, average speed, travel with stops, opposite directions, catch-up situations, delayed starts, round trips, and time relationships. Use hints when needed and review the explanation after each answer.

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1 Question 1 of 10
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A train travels 294 miles in 4.2 hours at a constant speed. What is its speed?

Hint: Use speed = distance ÷ time.
Explanation: Speed = 294 ÷ 4.2 = 70. The train travels at 70 miles per hour.
2 Question 2 of 10
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A cyclist rides at 18 miles per hour for 2.5 hours. How far does the cyclist travel?

Hint: Use distance = speed × time.
Explanation: Distance = 18 × 2.5 = 45 miles.
3 Question 3 of 10
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A bus travels 120 miles at 60 miles per hour, stops for 30 minutes, then travels another 90 miles at 45 miles per hour. What is the average speed for the entire trip, including the stop?

Hint: Average speed is total distance divided by total elapsed time, including the stop.
Explanation: First leg takes 120 ÷ 60 = 2 hours. The stop is 0.5 hour. Second leg takes 90 ÷ 45 = 2 hours. Total distance = 210 miles and total time = 4.5 hours. Average speed = 210 ÷ 4.5 ≈ 46.7 miles per hour.
4 Question 4 of 10
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Two cars leave the same town at the same time in opposite directions. One travels at 58 miles per hour and the other at 67 miles per hour. How far apart are they after 2.4 hours?

Hint: For opposite directions, add the speeds to get the separation rate.
Explanation: Their separation rate is 58 + 67 = 125 miles per hour. After 2.4 hours, distance apart = 125 × 2.4 = 300 miles.
5 Question 5 of 10
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A delivery truck leaves a warehouse at 8:00 AM traveling at 48 miles per hour. A car leaves the same warehouse at 9:30 AM on the same route traveling at 72 miles per hour. At what time does the car catch the truck?

Hint: First find the truck's head start. Then divide that distance by the difference in speeds.
Explanation: The truck has a 1.5-hour head start, so it travels 48 × 1.5 = 72 miles. The car gains at 72 - 48 = 24 miles per hour. Catch-up time after 9:30 AM is 72 ÷ 24 = 3 hours, so the car catches the truck at 12:30 PM.
6 Question 6 of 10
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A boat travels 84 miles downstream in 3 hours and returns the same 84 miles upstream in 4 hours. What is the boat's average speed for the entire round trip?

Hint: Do not average the two speeds directly. Use total distance divided by total time.
Explanation: Total distance = 84 + 84 = 168 miles. Total time = 3 + 4 = 7 hours. Average speed = 168 ÷ 7 = 24 miles per hour.
7 Question 7 of 10
Not answered

A runner covers the first 6 kilometers of a route at 12 km/h and the next 6 kilometers at 8 km/h. What is the runner's average speed over the 12-kilometer route?

Hint: The distances are equal, but the times are not. Find the time for each segment first.
Explanation: First segment time = 6 ÷ 12 = 0.5 hour. Second segment time = 6 ÷ 8 = 0.75 hour. Total time = 1.25 hours. Average speed = 12 ÷ 1.25 = 9.6 km/h.
8 Question 8 of 10
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Two hikers start 42 kilometers apart and walk toward each other. One walks at 4.5 km/h and the other at 6 km/h. How long will it take them to meet?

Hint: Because they move toward each other, their closing speed is the sum of their speeds.
Explanation: Closing speed = 4.5 + 6 = 10.5 km/h. Time = 42 ÷ 10.5 = 4 hours.
9 Question 9 of 10
Not answered

A plane is scheduled to cover 1,260 miles in 3 hours. After flying for 1 hour at 380 miles per hour, what speed must it average for the remaining 2 hours to arrive on schedule?

Hint: Find how much distance remains after the first hour, then divide by the remaining time.
Explanation: In the first hour the plane covers 380 miles. Remaining distance = 1,260 - 380 = 880 miles. It has 2 hours left, so required speed = 880 ÷ 2 = 440 miles per hour.
10 Question 10 of 10
Not answered

A commuter drives 36 miles to work at 45 miles per hour. To make the round-trip average speed exactly 60 miles per hour, what speed would be required for the 36-mile trip home?

Hint: First find the total time allowed for a 72-mile round trip averaging 60 mph. Then subtract the morning travel time.
Explanation: A 72-mile round trip at an average of 60 mph must take 72 ÷ 60 = 1.2 hours total. The morning trip takes 36 ÷ 45 = 0.8 hour, leaving 0.4 hour for the return. Required return speed = 36 ÷ 0.4 = 90 miles per hour.

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Route planning lab

Distance, speed, and time problems are really about matching motion to a timeline

These 10 problems include constant speed, travel with a stop, average speed, opposite directions, catch-up motion, delayed starts, round trips, meeting problems, schedule recovery, and a difficult round-trip average-speed target. Before calculating, decide whether the problem is about one traveler, closing distance, gaining distance, or total elapsed time.

Constant speedAverage speedOpposite directions Catch-upMeeting timeRound tripsSchedules
Elapsed-time timeline

Stops count when the question asks for average speed over the entire trip

The bus travels two legs with a 30-minute stop between them. That stop adds time but no distance.

First leg120 miles in 2 hours
Stop0.5 hour
Second leg90 miles in 2 hours
Whole trip210 miles in 4.5 hours
Opposite directions

When two travelers move apart, their separation grows at the sum of their speeds

This is why 58 mph and 67 mph create a separation rate of 125 mph.

After 2.4 hours: 125 × 2.4 = 300 miles apart.
Delayed start

Catch-up begins with a head start

The truck leaves 1.5 hours earlier at 48 mph. Before the faster car starts, the truck is already 72 miles ahead.

Head start: 48 × 1.5 = 72 miles
Closing speed: 72 − 48 = 24 mph
Catch-up time: 72 ÷ 24 = 3 hours
9:30 AM + 3 hours = 12:30 PM
Average-speed lab

Average speed is total distance divided by total time — not usually the average of two speeds

For the boat, the downstream and upstream distances are equal, but the travel times are different.

Total distance168 miles
Total time7 hours
Average speed24 mph
168 ÷ 7 = 24 miles per hour
Schedule recovery

If part of a trip is slower than planned, the remaining segment must compensate

Plane schedule

After one hour at 380 mph, 880 miles remain with 2 hours left.

880 ÷ 2 = 440 mph required

Round-trip target

A 72-mile round trip averaging 60 mph must take only 1.2 hours total.

36 ÷ (1.2 − 0.8) = 90 mph
After the quiz

Review the motion relationship that caused the error

Most mistakes come from combining speeds or times incorrectly, not from difficult arithmetic.

One travelerdistance, speed, time, scheduled arrival
Moving apartadd speeds to find separation rate
Catch-up / meetingrelative speed and initial distance
Average speedtotal distance divided by total elapsed time
Math Word Problems Rates & Proportions