SOLUTION: Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the

Question 513157: Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the average speed of the boat relative to the water.

***I need it worked out in detail please and thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the average speed of the boat relative to the water.
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Upstream DATA:
distance = 39 miles ; rate = b-5 mph ; time = d/r = 39/(b-5) hrs
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Downstream DATA:
distance = 39 miles ; rate = b+5 mph ; time = d/r = 39/(b+5) hrs
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Equation:
time + time = 16 hrs
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39/(b-5) + 39/(b+5) = 16
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1/(b-5) + 1/(b+5) = 16/39
[b+5+b-5]/b^2-25 = 16/39
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39*2b = 16b^2-400
39b = 8b^2-200
8b^2-39b-200 = 0
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Positive solution:
b = 8 mph (speed of the boat relative to the water)
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Cheers,
Stan H.
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