The Hudson River flows at a rate of 5 miles per hour a patro

The Hudson River flows at a rate of 5 miles per hour. a patrol boat travels 40 miles upriver and returns in a total time of 6 hours.What is the speed of the boat in still water?

Solution

Upstream DATA:
distance = 40 miles ; rate = b-5 : time = d/r = 40/(b-5) hrs.
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Downstream DATA:
distance = 40 miles ; rate = b+5 ; time = d/r = 40/(b+5) hrs.
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Equation:
time + time = 6 hrs.
40/(b-5) + 40/(b+5) = 6
40b+200 + 40b-200 = 6(b^2-25)
80b = 6b^2 - 150
3b^2 - 40b - 75 = 0
(3b+5)(b-15) = 0
Realistic Answer:
b = 15 mph (speed of the boat in still water)