Problem 2 · Compare trips to find a unit rate · 3 points
Made by AI and not reviewed by a real person.
A train travels at a constant speed. It takes 24 seconds to clear a 280 m tunnel and 32 seconds to clear a 440 m tunnel, each timed from when the train’s front enters to when its back exits. How long is the train?
- 480 m
- 280 m
- 200 m
- 330 m
- 160 m
Show a hint
- Compare the two crossings: what extra distance accounts for the extra time?
- In each crossing, the train travels the tunnel’s length plus its own length.
Show the answer and solution
Answer: C — 200 m
The longer tunnel adds 440 − 280 = 160 m to the train’s travel distance and 32 − 24 = 8 seconds to its time, so its speed is 20 m/s. In 24 seconds it travels 480 m; subtracting the 280 m tunnel gives a train length of 200 m. The tempting 480 m is the whole crossing distance, not the train’s length.