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I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

 May 21, 2024
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Let t be the time it takes to drive to the beach. We have

\(40\ mph\cdot t=55\ mph(t-25\ min)\\ 40t=55t-1375\ min\\ 15t=1375\ min\\ t=91\frac{2}{3}\ min\)

 

Now, we know that \(s=v\cdot t\) from our speed formulas. We just have to plug the values in!

 

We have 

\(s=v\cdot t=40\ mph\cdot 91\frac{2}{3}\ min\cdot \frac{h}{60\ min}\\ s=61 \frac{1}{9}\ miles\)

 

Thanks! :)

 May 21, 2024

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