Question

Person A leaves his home to visit his​ cousin, person​ B, who lives 162miles away. He travels at an average rate of 60miles per hour. One​ half-hour later, person B leaves her house to visit person​ A, traveling at an average rate of 72miles per hour. How long after person B leaves will it be before they​ meet?

Answer 1

Answer: 0.727 hours

Explanation:

Call A’s distance from A’s house “a(t)” when t hours have passed. Then a(t) = 60t, because distance = rate x time.

Call B’s distance from A’s house “b(t)”. Then b(t) = 162 - 72t, because they start 162 miles away and subtract miles as time elapses.

The time at which they meet will be when a(t) = b(t). (Think about it). So now we just solve for t:

60t = 162 - 72t

132t = 162

t = 1.227 hours.

HOWEVER this isn’t quite what they asked for. They want the time they meet since B left (not A), and since B left .5 hours after, we must subtract .5. Thus the answer is 0.727 hours.