Two trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more than that of the second train. What is the distance between these towns?

Suppose that the rate of the second train is x mph

the rate of the first one will be (x+26) mph

the distance covered by the trains will be:

Distance=speed*time

first train will be:

(2 4/5) * (x+26)

=14/5 (x+26)

=14/5x+364/5

Second train:

14/3 (x)

=14/3x

Given that both trains covered the same distance, then

14/5x+364/5=14/3x

364/5=28/15x

x=39 mph

thus the distance between the town will be:

14/3 (39)

=182 miles