Question 598033: On a weekend outing, Manuel rents a motorboat for 6hrs to travel down the river and back. The rental operator tells him to go for 2hrs downstream, leaving 4hrs to return upstream.
If the river current flows at a speed of 6mph,
how fast must Manuel travel in order to return in 6hrs?
(?)Mph
Answer by w_parminder(53)   (Show Source):
You can put this solution on YOUR website! Let the required speed of the boat be 'X' Mph and the boat cover a distance of 'Y' Miles in one direction.
Speed of the river current = 6 Mph,
So, downstream speed of the boat = X + 6
Time taken while travelling downstream = 2 Hrs
Using the formula, Distance = Time*Speed, we get
Y = 2*(X + 6)
Y = 2X + 12 (Equation 1)
upstream speed of the boat = X - 6
Time taken while travelling upstream = 4 Hrs
Using the formula, Distance = Time*Speed, we get
Y = 4*(X - 6)
Y = 4X - 24 (Equation 2)
Comparing equation 1 & 2, we get
4X - 24 = 2X + 12
4X - 2X = 12 + 24
2X = 36
X = 36/2
X = 18
So the required speed of the boat is 18 Mph
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