The speed of an electric train is 25% more than that of a steam-engine train.…
2024
The speed of an electric train is 25% more than that of a steam-engine train. How much time will the electric train take to cover a distance that the steam-engine train covers in 4 hours 25 minutes?
Answer: D. 3 8⁄15 hours — Concept: For a fixed distance, speed and time are inversely proportional. If speed is multiplied by a factor k, the required time is divided by k. A 25%…
- A.
3 1⁄10 hours
- B.
3 11⁄15 hours
- C.
3 11⁄12 hours
- D.
3 8⁄15 hours
Show answer & explanation
Correct answer: D
Concept: For a fixed distance, speed and time are inversely proportional. If speed is multiplied by a factor k, the required time is divided by k.
A 25% increase in speed changes the speed ratio to 125:100 = 5:4, so the corresponding time ratio is 4:5.
Convert the steam-engine train time: 4 hours 25 minutes = 4 + 25⁄60 = 53⁄12 hours.
Let the steam-engine train speed be v. Then the electric train speed is (5⁄4)v.
For the same distance, electric-train time = (53⁄12) × (v ÷ ((5⁄4)v)) = (53⁄12) × (4⁄5) = 53⁄15 hours.
Convert the improper fraction: 53⁄15 = 3 8⁄15 hours = 3 hours 32 minutes.
Cross-check: 3 hours 32 minutes = 212 minutes, and 212 × 5⁄4 = 265 minutes, which is 4 hours 25 minutes.
Result: The electric train takes 3 8⁄15 hours (3 hours 32 minutes).