The family car leaves the house 112
hours after the moving van and follows the same route. The moving van travels at an average speed of 45 miles per hour. The family car travels at an average speed of 60 miles per hour. After how many hours of driving will the family car catch up to the moving van?
Let $T$ be the time (in hours) it takes for the family car to catch up to the moving van.
In $T$ hours, the moving van travels $45T$ miles.
In $T+112$ hours, the family car travels $60(T+112)$ miles.
Since they are traveling the same route, the distance traveled by the moving van is equal to the distance traveled by the family car:
$45T = 60(T+112)$
Solve for $T$:
$45T = 60T + 6720$
$45T - 60T = 6720$
$-15T = 6720$
$T = \frac{6720}{-15}$
$T = -448$
Since $T$ cannot be negative, there must be a mistake in the setup of the problem. It seems that the family car will not be able to catch up to the moving van on this route.