During the first part of a trip, a canoeist travels 57 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2hrs. What was the speed on each part of the trip?

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Oddman answered
If the speed on the first part of the trip is given by "s", then the total time in hours can be computed as   57/s + 21/(s-5) = 2  Multiplying by s(s-5), we get   57(s-5) + 21s = 2s(s-5) Subtracting the left side from both sides, we get   0 = 2s^2 - 10s - 57s + 57*5 - 21s   0 = 2s^2 - 88s + 285 Using the quadratic formula, you find the solution to be   s = (-(-88) + √((-88)^2 - 4(2)(285)))/(2(2))   s = (44 + √1366)/2   s ≈ 40.480 mph  The first part of the trip was completed at 40.480 mph, and the second part was completed at 35.480 mph. _____ Check   57/40.480 + 21/35.480 ≈ 1.408 + .592 = 2.000 The canoe was not being paddled at that speed.

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