In a rowboat, it took Alice 6 hours to go 6 miles upstream, but she was able to return to her starting point in only 45 minutes. Assuming her rowing speed is constant, what was the speed of the current?
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When you row at a constant rate, and the speed of the current is x, when you are going with the current your boat is actually moving at (constant rate + current) and when you are going against the current, your boat is actually going at (constant rate - current)
d = rt
6 = (c - x)6
6 = (c + x)(.75) 45 minutes is 3/4 of an hour
6 = 6c - 6x distribute the 1st equation
6 = .75c + .75x distribute the 2nd equation
Solve the 1st equation for c and then we are going to substitute.
6 + 6x = 6c divide thru by 6
1 + x = c substitute into the other equation
6 = .75(1 + x) + .75x
6 = .75 + .75x + .75x
6 = .75 + 1.5x
5.25 = 1.5x
3.5 = x
Current is 3.5 mph