Question

Bob, Peter and Paul travel together. Peter and Paul are good hikers; each walks p miles per hour. Bob has a bad foot and drives a small car in which two people can ride, but not three; the car covers c miles per hour. The threee friends adopted the following scheme: They start together, Paul rides in the car with Bob, Peter walks. After a while, Bob drops Paul who walks on; Bob returns to pick up Peter, and then Bob and Peter ride in the car till they overtake paul. At this point, they change: Paul rides and Peter walks just as they started and the whole procedure is repeated as often as necessary.


A. How much progress (how many miles) does the company make per hour?

Answer 1

So basically we are asked average speed here. They are starting together. We will find after how much time and distance they are meeting again, and that will give us average speed.

Suppose in first turn Bob and Paul drive for (t) hours. So Bob and Paul will have covered distance of (ct) miles. And Peter will have covered distance of (pt) miles. Since Bob drops Paul and go back to receive Peter, (c>p) clearly. Distance between them will be (ct-pt)=t(c-p) miles. Since both Bob and Peter are moving in opposite direction, relative speed will be (c+p). So they will meet after hours. In this time Paul will have covered distance of . See below figure for reference.

As you can see from above figure, distance between Meeting point of Peter Bob and Paul will be . Now Peter Bob will drive at c miles per hour and Paul will walk at p miles per hour. So relative speed will be (c-p) as they are going in same direction. So they will meet after time hours. See final figure below.

So total distance after they are meeting:

                          

total time after they are meeting:

                          

So Average speed will be: