Question

A highway connects city A and city B and extends 2467 miles. Paul Simon begins in city A and drives at an average rate of 42 mph on the highway toward city B. At the same time John Smith begins in city B and drives on the highway at an average rate of 52 mph toward city A. If Paul and John maintain these average​ speeds, how long after they start will they​ meet?

Answer 1

26.24 hours

Step-by-step explanation:

Hi,

A very simple way to understand this problem is to imagine a number line. City A is zero and City B is 2467.

When Paul starts from A and moves towards B, he is moving in a positive direction. Similarly, when John starts from B and moves towards A, he is moving in the negative direction.

(Reminder: Distance = Speed × Time)

We can put this in an equation format:

0 → 2467 : 0 + 42×t

2467 → 0: 2467 - 52×t

Meeting at the same point means both these expressions must be equal to each other.

0 + 42t = 2467 - 52t

Solve this equation for t.

42t + 52t = 2467

94t = 2467

t = 26.24468 ≈ 26.24 hours

Hence, after travelling 26.24 hours at their respective speeds, Paul and John meet.