Question 386825: A boats crew rowed 7.5 miles downstream, with the current,in 1.5 hours. The return trip upstream, against the current,coverred the same distance, but took 2.5 hours.Find the crews rowing rate in still water at the rate of the current.
Found 2 solutions by gwendolyn, Alan3354:
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! To solve this problem, we will make use of the formula:
distance = rate*time
When traveling with a current, the rate of the current is added to the rate of the boat to get the effective rate. When traveling against a current, the rate of the current is subtracted from the rate of the boat to get the effective rate.
Let X be the rate of the boat.
Let Y be the rate of the current.
A boats crew rowed 7.5 miles downstream, with the current, in 1.5 hours.
Using the formula, distance = rate* time:
7.5 = (X + Y)*1.5
7.5 = 1.5X + 1.5Y
Let's solve for X by isolating the term with X:
7.5 - 1.5Y = 1.5X + 1.5Y - 1.5Y
7.5 - 1.5Y = 1.5X
Divide both sides by 1.5:
(7.5)/(1.5) - (1.5Y)/(1.5) = (1.5X)/(1.5)
5 - Y = X
The return trip upstream, against the current,coverred the same distance, but took 2.5 hours [ed -- originally stated "miles" but must be "hours"].
Using the formula, distance = rate* time (Note: the return trip distance is the same as the trip downstream):
7.5 = (X - Y)*2.5
7.5 = 2.5X - 2.5Y
Substitute the value of X from the first equation:
7.5 = 2.5(5 - Y) - 2.5Y
7.5 = 12.5 - 2.5Y - 2.5Y
7.5 = 12.5 - 5Y
Subtract 12.5 from both sides:
7.5 - 12.5 = 12.5 - 5Y - 12.5
-5 = -5Y
Divide both sides by -5:
(-5)/(-5) = (-5Y)/(-5)
1 = Y
Substitute the value of Y back into the first equation:
5 - Y = X
5 - 1 = X
4 = X
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! 7.5/1.5 = 5 mph downstream
7.5/2.5 = 3 mph upstream
The rowing speed is the average
= (5+3)/2 = 4 mph
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The current is the difference = 1 mph
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