SOLUTION: a boat travels 80km upstream and then returns to its starting point. The entire trip takes 3.6h. if the speed of the current is 10km/h, determine the speed of the boat in still wat

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Question 15821: a boat travels 80km upstream and then returns to its starting point. The entire trip takes 3.6h. if the speed of the current is 10km/h, determine the speed of the boat in still water.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = speet of the boat in still water.
x+10 = speed of the boat going downstream.
x-10 = speed of the boat going upstream.

The equation is based upon the time of the boat to go upstream and then downstream.

Time upstream = D%2Fr Time downstream = D%2Fr

Total time = Time up + Time down = 3.6 hours
80%2F%28x-10%29+%2B+80%2F%28x%2B10%29+=+3.6+

Multiply both sides of the equation by the LCD = (x-10)(x+10), and the result is:
80(x+10) + 80(x-10) = 3.6(x-10)(x+10)
80x +800 + 80x - 800 = 3.6(x^2 - 100)
160x = 3.6x^2 - 360

Set equal to zero, since it is a quadratic equation:
0 = 3.6x^2 - 160x - 360
Use quadratic equation solver or calculator:
x+=+%28160+%2B-+sqrt%28+160%5E2%2B4%2A3.6%2A360+%29%29%2F%282%2A3.6%29+
x+=+%28160+%2B-+sqrt%2830784%29%29%2F+7.2+
x+=+%28160+%2B-+175.4537%29%2F7.2+ (approximately!)

x must be a postive number, so forget the negative value,
x=+%28160+%2B+175.4537%29%2F7.2
x+=+46.49+mph in still water.
x+10 = 56.49 mph downstream
x-10 = 36.49 mph upstream

As a check, calculate the equation for time upstream and downstream:
80%2F36.49+%2B+80%2F56.49. The answer comes out to about 3.6 hours.

R^2 at SCC