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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?

 Jun 9, 2024
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Let's use the "distance = rate (or speed) times time". Let's suppose that d represents the distance to the beach and t represents the time taken to drive to the beach at 40 mph.Then we can represent what we said as these equations:

\(d = 40 \times t\)

\(d = 55 \times (t - 5/12)\)

We can now simplify these equations and solve for d like this:

\(d = 55t - 275/12\)

\(55t - 275/12= 40t\)

\(15t= 275/12\)

\(t = 55/36\)

\(d = 55/36 \times 40\)

\(d = 550/9\)

 

So the distance you will drive will be 550/9 miles.

 Jun 9, 2024

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