Question

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?

Answer 1

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