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Question 408934: I am looking for some hep on this algebra problem for my child please.
Please show work: The Connecticut River flows at a rate of 4km/h for the length of a popular senic route. In order for a cruiser to travel 60 km upriver and then return in a total of 8 hr, how fast must the boat be able to travel in still water?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The Connecticut River flows at a rate of 4km/h for the length of a popular senic route. In order for a cruiser to travel 60 km upriver and then return in a total of 8 hr, how fast must the boat be able to travel in still water?
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applying the distance formula:
d = rt
solving for time (t) we get:
t = d/r
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Let x = speed in still water
then
"time upstream" + "time downstream" = "total time"
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60/(x-4) + 60/(x+4) = 8
multiplying both sides by (x-4)(x+4) we get:
60(x+4) + 60(x-4) = 8(x-4)(x+4)
60x+240 + 60x-240 = 8(x^2-16)
120x = 8x^2-128
0 = 8x^2-120x-128
dividing both sides by 8:
0 = x^2-15x-16
factoring:
0 = (x-16)(x+1)
x = {16,-1}
we can throw out the negative solution leaving:
x = 16 mph
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