Let's solve each of the
Speed, Time, and Distance word problems step by step. We'll use the basic formula:
>
Speed = Distance ÷ Time
>
Distance = Speed × Time
>
Time = Distance ÷ Speed
---
Problem 1:
A cyclist covers a distance of 30 miles in 4 hours. Calculate his speed.
Solution:
Given:
- Distance = 30 miles
- Time = 4 hours
Use the formula:
Speed = Distance ÷ Time
= 30 ÷ 4
=
7.5 mph
✔ Answer: 7.5 miles per hour
---
Problem 2:
A car takes 3 hours to cover a distance, if it travels at a speed of 50 mph. What should be its speed to cover the same distance in 4.5 hours?
Step 1: Find the distance first.
Distance = Speed × Time
= 50 mph × 3 hours
=
150 miles
Step 2: Find new speed to cover 150 miles in 4.5 hours
Speed = Distance ÷ Time
= 150 ÷ 4.5
=
33.33... mph (or
33⅓ mph)
✔ Answer: 33.33 mph (or 33⅓ mph)
---
Problem 3:
Bill roller skates for 2 hours with a constant speed of 15 km/h and then for another 1 hour 25 minutes with a constant speed of 18 km/h. What distance did he go?
Step 1: First part – 2 hours at 15 km/h
Distance₁ = Speed × Time
= 15 km/h × 2 h
=
30 km
Step 2: Second part – 1 hour 25 minutes at 18 km/h
Convert 1 hour 25 minutes to hours:
25 minutes = 25/60 = 5/12 ≈ 0.4167 hours
So, total time = 1 + 0.4167 =
1.4167 hours
Distance₂ = 18 km/h × 1.4167 h
≈ 18 × 1.4167 =
25.5 km
Total distance = 30 + 25.5 = 55.5 km
✔ Answer: 55.5 kilometers
---
Problem 4:
A train travels 40 miles with a constant speed of 40 mph and another 60 miles with a constant speed of 50 mph. How much time in total does it take to travel these distances?
First segment: 40 miles at 40 mph
Time₁ = Distance ÷ Speed
= 40 ÷ 40 =
1 hour
Second segment: 60 miles at 50 mph
Time₂ = 60 ÷ 50 =
1.2 hours
Convert 0.2 hours to minutes: 0.2 × 60 = 12 minutes → So 1.2 hours = 1 hour 12 minutes
Total time = 1 + 1.2 = 2.2 hours
Or: 2 hours 12 minutes
✔ Answer: 2.2 hours (or 2 hours 12 minutes)
---
Problem 5:
A car travels at an average speed of 60 mph. How long will it take for the car to travel 11 miles? Give your answer in minutes.
Time = Distance ÷ Speed
= 11 ÷ 60 =
0.1833... hours
Now convert to minutes:
0.1833 × 60 =
11 minutes
✔ Answer: 11 minutes
---
Problem 6:
Rodney rides his bike for 1 hour 30 minutes with a constant speed of 10 km/h and then for another 1 hour 10 minutes with a constant speed of 20 km/h. What distance did he go?
First part: 1 hour 30 minutes at 10 km/h
Convert time to hours:
30 minutes = 0.5 hours → Total = 1.5 hours
Distance₁ = 10 × 1.5 =
15 km
Second part: 1 hour 10 minutes at 20 km/h
10 minutes = 10/60 = 1/6 ≈ 0.1667 hours → Total = 1.1667 hours
Distance₂ = 20 × 1.1667 ≈
23.33 km
Total distance = 15 + 23.33 = 38.33 km
✔ Answer: 38.33 kilometers
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✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | 7.5 mph |
| 2 | 33.33 mph (or 33⅓ mph) |
| 3 | 55.5 km |
| 4 | 2.2 hours (or 2 hours 12 minutes) |
| 5 | 11 minutes |
| 6 | 38.33 km |
Let me know if you'd like this as a printable solution sheet!
Parent Tip: Review the logic above to help your child master the concept of speed problems worksheets.
