Sheila leaves on a long trip driving at a steady rate of 30 miles per hour. Her sister Allison leaves from the same location traveling to the same destination 2 hours later. She drives at a steady rate of 45 miles per hour. How long after Allison leaves home will she catch up to Sheila?

Question

Sheila leaves on a long trip driving at a steady rate of 30 miles per hour. Her sister Allison leaves from the same location traveling to the same destination 2 hours later. She drives at a steady rate of 45 miles per hour. How long after Allison leaves home will she catch up to Sheila?

6 hours

5 hours

4 hours

2 hours

Answer 1

Let t be the time it takes for Allison to catch up to Sheila.

Since Sheila drives at 30 mph for t+2 hours, she travels 30(t+2) miles.
Allison drives at 45 mph for t hours, she travels 45t miles.

When Allison catches up to Sheila, they would have traveled the same distance.

So, 30(t+2) = 45t
30t + 60 = 45t
15t = 60
t = 4

Therefore, Allison will catch up to Sheila 4 hours after she leaves home.

The answer is 4 hours.