Worksheet with distance-rate-time word problems and handwritten solutions.

Let’s solve each problem one by one, step by step. We’ll use the formula:

Distance = Rate × Time
or rearranged as needed:
Rate = Distance ÷ Time
Time = Distance ÷ Rate

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Problem 1:

> An aircraft carrier made a trip to Guam and back. The trip there took three hours and the trip back took four hours. It averaged 6 km/h on the return trip. Find the average speed of the trip there.

We know:
- Return trip time = 4 hours
- Return trip rate = 6 km/h
→ So, distance back = 6 × 4 = 24 km

Since it’s the same trip there and back, distance there is also 24 km.

Trip there took 3 hours → so rate there = 24 ÷ 3 = 8 km/h

✔ Final Answer for #1: 8 km/h

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Problem 2:

> A passenger plane made a trip to Las Vegas and back. On the trip there it flew 432 mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took nine hours?

Return trip:
- Rate = 480 mph
- Time = 9 hours
→ Distance = 480 × 9 = 4320 miles

Same distance going there → so time there = distance ÷ rate = 4320 ÷ 432 = 10 hours

✔ Final Answer for #2: 10 hours

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Problem 3:

> A cattle train left Miami and traveled toward New York. 14 hours later a diesel train left traveling at 45 km/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle train's average speed?

Diesel train:
- Speed = 45 km/h
- Time = 4 hours
→ Distance covered = 45 × 4 = 180 km

Cattle train had a 14-hour head start + 4 more hours = 18 hours total

It traveled the same 180 km in 18 hours → speed = 180 ÷ 18 = 10 km/h

✔ Final Answer for #3: 10 km/h

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Problem 4:

> Jose left the White House and drove toward the recycling plant at an average speed of 40 km/h. Rob left some time later driving in the same direction at an average speed of 48 km/h. After driving for five hours Rob catches up with Jose. How long did Jose drive before Rob caught him?

Rob:
- Speed = 48 km/h
- Time = 5 hours
→ Distance = 48 × 5 = 240 km

Jose was driving at 40 km/h and also traveled 240 km when caught.

So Jose’s time = 240 ÷ 40 = 6 hours

✔ Final Answer for #4: 6 hours

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Problem 5:

> A cargo plane flew to the maintenance facility and back. It took one hour less time to get there than it did to get back. The average speed on the trip there was 220 mph. The average speed on the way back was 200 mph. How many hours did the trip there take?

Let x = time to get THERE (in hours)
Then time BACK = x + 1

Distance there = 220 × x
Distance back = 200 × (x + 1)

Distances are equal → set them equal:

220x = 200(x + 1)
220x = 200x + 200
220x - 200x = 200
20x = 200
x = 10

✔ Final Answer for #5: 10 hours

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Problem 6:

> Kali left school and traveled toward her friend’s house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.

Let x = hours Matt travels
Then Kali has been traveling x + 1 hours

Kali’s distance = 40 × (x + 1)
Matt’s distance = 50 × x

They’re going opposite directions → add distances:

40(x + 1) + 50x = 400
40x + 40 + 50x = 400
90x + 40 = 400
90x = 360
x = 4

✔ Final Answer for #6: 4 hours

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Final Answer:
1) 8 km/h
2) 10 hours
3) 10 km/h
4) 6 hours
5) 10 hours
6) 4 hours