In how many hours will the second car overtake the first?

Question

A car leaves a town traveling at 72 km/h. An hour later, a second car leaves the same town, on the same road, traveling at 90 km/h. In how many hours will the second car overtake the first?

Answer 1

Distance = (Rate)(Time)

Let x = number of hours driven by car 1 when the second car catches up

Then x - 1 = number of hours driven by car 2

The second car catches up to the first when the distances are the same

So, 72x = 90(x-1)

72x = 90x - 90

18x = 90

x = 5 hours

The second car catches up to the first 4 hours after starting, or 5 hours after the first car departs.