Question

A man starts out on a trip driving his car at a constant rate of 48 mph. A man riding a motorcycle starts out on the same route 112 hours later, traveling at a constant rate of 64 mph. How long will the car have been traveling when the motorcycle catches up?

Answer 1

6 hours on edge

Explanation:

Answer 2

4.5 hours

Explanation:

Let x hours be the time needed the motorcycle to catch the car.

Car:

Time
`=t+1(1)/(2)` hours

Rate = 48 mph

Distance
`=48\cdot \left(t+1(1)/(2)\right)` miles

Motorcycle:

Time
`=t` hours

Rate = 64 mph

Distance
`=64\cdot t` miles

The distance traveled is the same, so

`48\cdot \left(t+1(1)/(2)\right)=64\cdot t\\ \\48t+72=64t\\ \\72=16t\\ \\t=4.5\ hours`