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# Travelling with guys who dislike each other.

## Question

Bob, Peter, and Paul desire to travel together. Peter and Paul dislike each other and as a result refuse to ride with one another. Bob has agreed to drive each one following a creative system. With the car covering c miles per hour, the three people adopted the following scheme: Paul rides in the car with Bob, Peter walks. After a while, Bob drops off Paul, who begins walking; 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. Both Paul and Peter walk at the same speed, covering p miles per hour.

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

B. What fraction of the travel time does the car carry only person?

## Recommended Posts

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1. c*(c+3p)/(3c+p)

2. (c-p)/(3c-p)
3. Paul and peter will walk same distance regardless of c, p and how far Bob drops Paul.

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