Sophie drove 225mi south through the Smokey mountains. Snow during her trip made her average speed on the return trip 30mph slower. The total driving time was 8hr. Find Sophie’s average speed on each part of the trip.

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Sophie drove 225mi south through the Smokey mountains. Snow during her trip made her average speed on the return trip 30mph slower. The total driving time was 8hr. Find Sophie’s average speed on each part of the trip.

Mathematics
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Let the speed on the first stage of the trip be t mph. Then the speed on the return trip is (t - 30) mph. Time for the first stage of the trip = 225/t. Time for return stage of the trip = 225/(t - 30). Total time for the complete journey is given as 8 hours. Therefore we can write: \[\large \frac{225}{t}+\frac{225}{t-30}=8\] This last equation can be rearranged into a quadratic which can be solved to find the value of t.

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