Question

49) A car leaves town at 50 miles per hour. Two hours later, a second car, traveling 70 miles per hour, leaves along the same route as the first car. How long would it take for the second car to overtake the first car?

Answer 1

Let H represent the number of hours that must pass before the second car catches up with the first. This is a rate x time = distance problem.

50 m/h H = 70 m/h (H-2)

50H = 70(H-2) = 70H - 140
This is by virtue of the distributive property of multiplication over addition.

0 = 20H - 140
We subtract 50H from each side.

140 = 20H
We add 140 to each side.

7 = H
We divide each side by 20.

Seven hours is required for the two cars to encounter each other.