Bunuel wrote:
An express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers. A local train traveled at an average speed of 50 kilometers per hour, stopping for 1 minute after every 25 kilometers. If the trains began traveling at the same time, how many kilometers did the local train travel in the time it took the express train to travel 600 kilometers?
(A) 300
(B) 305
(C) 307.5
(D) 1200
(E) 1236
We are given that the express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers.
Let’s determine how many intervals of 75 km are in 600 km.
600/75 = 8
Since on the 8th interval the train will have stopped, the express train stopped for 3 x 7 = 21 minutes during the trip.
We also see that, without stopping, it takes the express train 6 hours to travel 600 km.
Thus, the total time spent by the express train was 6 hours and 21 minutes.
For the local train, we need to figure out how many minutes were spent on stopping in 6 hours and 21 minutes. Since the local train’s speed is 50 kmph and it travels every 25 km before it stops, it travels every 30 minutes before it stops. In 6 hours (ignoring the 21 minutes first), there are 12 intervals of 30 minutes and 11 stoppings of 1 minute, thus making a total of 6 hours and 11 minutes.
We see that we still have 10 minutes left to make up the 6 hours and 21 minutes. In these 10 minutes, the local train will stop for 1 minute first (after the 12th interval of 30-minute traveling) and then travels for 9 more minutes. Thus the actual travelling time of the local train (the time it’s moving) is 6 hours and 9 minutes, and during this time, it has traveled:
6 x 50 + 9/60 x 50 = 300 + 7.5 = 307.5 miles
Answer: C