At lunchtime, a man called his wife from his office to tell her that they needed to switch vehicles so that he could use the family van to pick up some building materials after work. The wife then left their home, traveling towards his office in their van at 32 mph. At the same time, the husband left his office in his car, traveling towards their home at 47 mph. If his office is 47.4 miles from their home, how long will it take them to meet so that they can switch vehicles?

Question

Quizplus · Accepted Answer

To find the time it takes for the couple to meet, we need to first determine how far they are from each other initially. We do this by adding their individual distances traveled, which we can find using the formula:

distance = rate × time

Let t be the time it takes for them to meet. Then, the wife travels a distance of 32t miles, while the husband travels a distance of 47t miles. So, initially, they are:

47.4 - (32t + 47t) miles apart

Simplifying this expression, we get:

47.4 - 79t miles apart

To find the time it takes for them to meet, we need to set this expression equal to zero (i.e., when they are at the same location). Thus, we have:

47.4 - 79t = 0

Solving for t, we get:

t = 0.6 hours

Therefore, the answer is C) 0.6 hr.

At Lunchtime, a Man Called His Wife from His Office