Traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12mph and the total trip took 3 hours and 40 minutes, find the average speed of the boat relative to the water. The boat had an average of what speed in MPH?

Question

Alexa Merritt

Mathematics

27 August, 08:53

Traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12mph and the total trip took 3 hours and 40 minutes, find the average speed of the boat relative to the water. The boat had an average of what speed in MPH?

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Hanna Bender · Answer 1

Traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12 mph and the total trip took 3 hours and 40 minutes.

Let S = boat speed in still water then (s + 12) = downstream speed (s - 12) = upstream speed

Given Time = 3 hours 40 minutes = 220 minutes = (220/60) h = (11/3) h Time = Distance/Speed

33 / (s + 12) + 33 / (s-12) = 11/3 3{33 (s-12) + 33 (s + 12) } = 11 (s+12) (s - 12) 99 (s - 12 + s + 12) = 11 (s^{2} + 12 s - 12 s - 144) 99 (2 s) = 11 (s^{2} - 144) 198 s/11 = (s^{2} - 144) 18 s = (s^{2} - 144) (s^{2} - 18 s - 144) = 0 s^{2} - 24 s + 6 s - 144 = 0 s (s - 24) + 6 (s - 24) = 0 (s - 24) (s + 6) = 0 s - 24 = 0, s + 6 = 0 s = 24, s = - 6 Answer) s = 24 mph is the average speed of the boat relative to the water.