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 Question from Christian, a student: Question: Two cars are racing to a fixed point and back. One car travels 70 MPH both ways While the other travels 60 MPH there and 80 MPH back, which car won the race? It is not a tie.

Hi Christian,

The important fact here is that

$\mbox{ rate} = \frac{\mbox{distance}}{\mbox{time}}$

Suppose that the distance from the start to the fixed point is $d$ miles, the time it takes to travel this distance at 70 mph is $t$ hours, the time it takes to travel this distance at 60 mph is $t_{1}$ hours and the time it takes to travel this distance at 80 mph is $t_{2}$ hours.

Use the fact that rate is distance over time to find $t, t_1$ and $t_2$ as functions of $d$ and ask is $2t = t_1 + t_{2}?$

Penny

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