Thomas takes the train to work every morning and the bus back home every night.

Question

While the train goes quicker due to a lack of traffic, the route it take is 25% longer than the route of the bus, and as a result, their travel times are equal. If the bus travels for an hour and 36 minutes at 50 miles an hour, what is the velocity (rate) of the train in miles per minutes?

A)25/24

B)125/2

C)60

D)1

Answer 1

50/x = 100/125; x = 50·125/100 = 125/2 mi/h = (125/2)/60 = 125/120 = 25/24 mi/min

Answer 2

Let x = velocity of the train

Distance = (Rate)(Time). So the distance traveled by the bus = (50)(1.6) = 80 miles

Distance traveled by the train = 80 + 0.25(80) = 100 miles

So, 100 = 1.6x

x = 62.5 miles per hour = (62.5 mi/hr)(1 hr / 60 min) = 1.041666 mi/min) = 25/24 mi / min