### Question Description

A boats crew rowed 7.5 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 2.5 hours. Find the crews rowing rate in still water and the rate of the current.

## Explanation & Answer

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**distance = rate*time **

Let X be the rate of the boat.

Let Y be the rate of the current.

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,covered the same distance, but took 2.5 hours

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

5 - Y = X

5 - 1 = X

4 = X

7.5/1.5 = 5 mph downstream

7.5/2.5 = 3 mph upstream

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