Lapping Racing Drivers

Good – or more dangerous – racing drivers are faster than other racing drivers. Towards the end of a race, the slower drivers may find themselves being lapped by other racing drivers who have completed one more circuit than they have.

If the speeds of the racing drivers areandwithon a circuit ofmiles, how long will it be before the faster driver laps the slower?

The faster driver travelsmph faster than the slower. Suppose the time for the slower driver to be lapped ishours, then the faster driver will have travelledmiles further.

We can use the equationwithand speed equal to the relative speed of the drivers,to giver

Suppose thatand

The time for the slower driver to be lapped is then

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