SOLUTION: A boat traveled downstream a distance of 128mi and then came right back. If the speed of the current was 7mph and the total trip took 5hrs and 20mins, find the average speed of th

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Question 624255: A boat traveled downstream a distance of 128mi and then came right back. If the speed of the current was 7mph and the total trip took 5hrs and 20mins, find the average speed of the boat relative to the water.
Answer by lwsshak3(11628) (Show Source):
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A boat traveled downstream a distance of 128mi and then came right back. If the speed of the current was 7mph and the total trip took 5hrs and 20mins, find the average speed of the boat relative to the water.
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let x=speed of boat relative to water (0 current)
x+7= speed of boat downstream
x-7= speed of boat downstream
travel time=distance/speed
5hr and 20 min=5 and 1/3 hr=16/3 hr
128/(x+7)+128/(x-7)=16/3
LCD: 3(x+7)(x-7)
3*128(x-7)+3*128(x+7)=16(x+7)(x-7)
384x-2688+384x+2688=16(x^2-49)=16x^2-784
16x^2-768x-784=0
x^2-48x-49=0
(x-49)(x+1)=0
x=-1, (reject, x>1)
or
x=49
speed of boat relative to water=49 mph