Question 285655
Jen’s boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water. 
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Upstream DATA:
distance = 45 miles ; rate = b-3 mph ; time = d/r = 45/(b-3) hrs.
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Downstream  DATA:
distance = 45 miles ; rate = b+3 mph ; time = d/r = 45/(b+3) hrs
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Equation:
time + time = 8 hr
45/(b-3) + 45/(b+3) = 8
Multiply thru by (b^2-9) to get:
45(b+3) + 45(b-3) = 8(b^2-9)
90b = 8b^2 - 72
Rearrange:
8b^2 - 90b - 72 = 0
4b^2 -45b - 36 = 0
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(b-12)(4b+3) = 0
Positive solution:
b = 12 mph (boat speed in still water)
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Cheers,
Stan H.
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