What is crews. Rowing rate in still water mph? What is rate of current mph?

Mathematics
Tutor: None Selected Time limit: 1 Day

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.

Jun 7th, 2015

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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


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 7th, 2015

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