# Joe the incremental car pusher

Whenever I call my friend Joe, he pushes a car down a road. (Assume the road is flat and has no other cars on it, and that the car has no brakes.)

The car Joe's pushing has to cover a very precise distance by the end of the day.

At the start of the day, Joe and I have to agree on the frequency at which I'll call him until he's reached the preagreed distance, and the distance he'll push the car by every time I call him. (BTW, Joe is the name of my computer program's function).

Given:

• the total distance that Joe needs to cover.

• the total amount of time that Joe has to take to cover that distance.

• that the frequency at which I will call Joe is arbitrarily chosen before he starts pushing the car, but stays the same until he's reached the preagreed distance.

Find the equation that will give me the distance Joe has to push the car by every time I call him.

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Let the day be 24 hours; call him $f$ times an hour; let the total distance be $d$; let the push each time be $p$; then the equation relating everything is $d=24pf$. Solving for $p$ you get $p=d/(24f)$.