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 the Express train starts will it overtake the Local? Write the time as a decimal.

{
hrs.}

Answer 1

Step 1: Define the variables:
Let x be the number of hours that the Express train runs.

Step 2: Set up an equation:
Since the Local train started an hour and a half earlier, it has already been running for x + 1.5 hours when the Express train starts. Distance = Rate × Time, so:
35(x + 1.5) = 56x

Step 3: Solve the equation:
35x + 52.5 = 56x
52.5 = 56x - 35x
52.5 = 21x
x = 52.5/21
x ≈ 2.5

Therefore, the Express train will overtake the Local train approximately 2.5 hours after it starts.