A takes 2 hours more than B to walk P km, but if A doubles his speed, then he…
2023
A takes 2 hours more than B to walk P km, but if A doubles his speed, then he can make it in one hour less than B. How much time does B require for walking P km?
Answer: A. 4 hours — ConceptFor a fixed distance, time is inversely proportional to speed. Therefore, doubling a person's speed halves that person's travel time. ApplicationLet…
- A.
4 hours
- B.
3 hours
- C.
5 hours
- D.
3.5 hours
Show answer & explanation
Correct answer: A
Concept
For a fixed distance, time is inversely proportional to speed. Therefore, doubling a person's speed halves that person's travel time.
Application
Let B's time for P km be t hours. Since A takes 2 hours more, A's time at the original speed is t + 2 hours.
When A doubles his speed, his time becomes (t + 2)/2 hours.
The doubled-speed time is 1 hour less than B's time, so (t + 2)/2 = t - 1.
Multiplying by 2 gives t + 2 = 2t - 2, hence t = 4.
Cross-check
If B takes 4 hours, A originally takes 6 hours. Doubling A's speed halves 6 hours to 3 hours, which is exactly 1 hour less than B's time. Therefore, B requires 4 hours.