Bunuel
A train is traveling at a constant speed from city A to city B. Along this trip the train makes three one-hour stops and reaches city B. At city B the train is stopped again for 1 hour. After that the train makes the return trip from city B to city A at a constant speed which is twice the speed of the first trip. Along this return trip the train makes ten thirty minutes stops and reaches city A. If both trips took the same amount of time, how many hours was the roundtrip?
A. 14
B. 15
C. 16
D. 17
E. 18
Stoppage Time from A to B = 3*60 mins = 180 mins = 3 hrs
Stoppage Time from B to A = 10*30 mins = 300 mins = 5 hrs
Stoppage time from A to B is 2 hrs less than stoppage time from B to A. But both trips took the exact same total time.
This means that the actual travel time from A to B was 2 hrs extra.
Think about it this way:
Two people X and Y must take the same time to travel the same distance. Speed of X is less than the speed of Y. What will X do to cover the distance in same time as Y? X will take fewer breaks. X will continue moving for longer to make up for this low speed. So if X needed 4 hrs to actually cover the distance and Y needed only 2 hrs, X will take only a 3 hrs break compared with Y who plans to take a 5 hour break in between. So the shorter break that X takes is to compensate for the longer time he will need to travel. Since he will need 2 hrs extra to travel, he will take a break which is shorter by 2 hrs.
In the question we are given that A to B break time is 2 hrs less. It means that A to B travel time was 2 hrs extra.
Since speeds in the two trips are in the ratio 1:2, travel time taken would be in the ratio 2:1. The difference of 1 is actually 2 hrs so travel time from A to B is 2*2 = 4 hrs and travel time from B to A is 1*2 = 2 hrs.
Total Time for Return Trip = Total travel time + Stoppage Time + Break Time at B = (4 + 2) hrs + (3 + 5) hrs + 1 hr = 15 hrs
Answer (B)