A slow train leaves the station 2 hrs later a fast train wit

A slow train leaves the station, 2 hrs later a fast train, with double the speed of the slow train, leaves the station and catches up with the slow train after traveling 180 mi. Find the speed of both trains.

Solution

When the two trains meet, they both will have traveled 180 miles
:
Let s = speed of the slow train
Let 2x = speed of the fast train
:
Write a time equation:
t = dist/ speed
:
slow train time = fast train time + 2 hr
180/s = 180/2s + 2
180/s = 90/s + 2
:
Get rid of the denominators, mult equation by 2s
180 = 90 + 2s
180 - 90 = 2s
2s = 90
s = 45 mph is the slow train.