Question

A train traveling nonstop to its destination is able to make the trip at an average speed of 70 miles per hour. On the return trip, the train makes several stops and is only able to average 40 miles per hour. If the return trip takes three hours longer than the initial trip to the destination, then what is the travel time for the return trip? Specify the units in your answer!

Answer 1

Return trip travel time: 7h

Explanation:

Let d be the distance.

Index 1 refers to initial trip, index 2 refers to the return trip.

v1=70mi/h

v2=40mi/h

t2=t1+3h, or t1=t2-3h (travel times)

d=v1×t1=v2×t2

v1×(t2-3)=v2×t2

v1 t2 -3 v1=v2 t2

v1 t2 - v2 t2=3 v1

t2(v1-v2)=3v1

t2=3v1/(v1-v2)

Or

t2=3×70/(70-40)=3×70/30=7h