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 12 hours later, traveling at a constant rate of 64 mph. How long will the car have been traveling when the motorcycle catches up?
Let t be the number of hours that the person drives his car. Therefore, his total distance is 48·t.
The man on the motorcycle starts out 12 hours later. Therefore, his amount of time is t - 12 and his total distance is 64·(t - 12).
Since these two distances are equal: 48t = 64(t - 12)
Solving: 48t = 64t - 768
Subtracting 64t from both sides: -16t = -768
Dividing both sides by -16: t = 48 hours (for the car)