Use the three steps to solve the problem.

A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after it starts will the Express overtake the Local?

The answer is 2.5h.

Step 1. Express distances (d1 and d2, d1 = d2 = d) using the formula for the speed v = d/t

Step 2. Make the system of equations.

Step 3. Solve the system of equations and express t2

Step 1.

Local train parameters:

rate: v1 = 35 mph

time: t1

distance: d

v1 = d/t1

d = v1 * t1 = 35*t1

Express train parameters:

rate: v2 = 56 mph

time: t2 = t1 - 1.5 h (because it is leaves hour and a half later then the local)

distance: d

v2 = d/t2

d = v2 * t2 = 56 * (t1 - 1.5)

Step 2. Make the system of equations:

d = 35*t

d = 56 * (t - 1.5)

Step 3. Solve the system of equations by using substitution method and calculate t2:

35t = 56 (t1 - 1.5)

35t = 56t1 - 56*1.5

35t = 56t1 - 84

84 = 56t1 - 35t1

84 = 21t1

t1 = 84/21

t1 = 4

t2 = t1 - 1.5

t2 = 4 - 1.5

t2 = 2.5 h