A truck crosses the county line at 60 mph. Please help me solve this

Question

A truck crosses the county line at 60 mph. Five minutes later, a sheriff crosses the border in hot pursuit,
driving at 90 mph. How far from the border will the sheriff overtake the trucker?

Answer 1

We know that distance = rate x time. The truck is travelling for t minutes. The sheriff is going for t-5 minutes. Since the speeds are given in mph, we need to divide them by 60 to make them miles per minute.

The speeds are 1 mpm for the truck and 1.5 mpm for the sheriff.

 

The truck goes 1t miles in his time, and the sheriff goes 1.5(t-5) miles in his time. The two distances are the same, since they represent the distance from the county line to the point where the vehicles come together.

 

So we have the equation  1t= 1.5(t-5)

 

Use the distributive property to remove the parentheses:

 

     1t = 1.5t - 7.5

 

Subtract 1.5t from both sides to isolate the variable.

 

     -.5t = -7.5

 

Divide both sides by -.5 to get  -7.5/-.5 = 15 minutes

 

The truck has gone  1 mile per minute for 15 minutes, which is 15 miles.

To check, see that the sheriff went 1.5 mpm for 10 minutes, which is also 15 miles.