Two cities are 45 miles apart. two trains, with speeds of 70 mph and 60 mph, leave the two cities at the same time so that one is catching up to the other. how long after the trains leave will the distance between them be 10 miles? a how many solutions does the problem have?

The correct answer is  27' (minutes). The problem actually has only one solution.

Explanation:

We have to part from the basic speed-distance-time formula:

s=d/t

The time until they are distanced 10 miles is the same since the two trains leave at the same moment. We will call that time: t We will call the first train: A d1 is the distance train A traveled until it is distanced 10 miles from train B

70=d1/t

70t = d1

We will call the second train: B d2 is the distance train B traveled until it is distanced 10 miles from train A

60=d2/t

60t = d2

So, the distance between A and B when the trains leave is: 45 miles

d1 + d2 + 10 = 45

70t + 60t = 35

130t = 35

t=27’

The problem actually has only one solution.