SOLUTION: Renee rows a boat downstream for 27 miles. The return trip upstream took 24 hours longer. If the current flows at 4 mph, how fast does Renee row in still water?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Renee rows a boat downstream for 27 miles. The return trip upstream took 24 hours longer. If the current flows at 4 mph, how fast does Renee row in still water?      Log On


   

Question 1030876: Renee rows a boat downstream for 27 miles. The return trip upstream took 24 hours longer. If the current flows at 4 mph, how fast does Renee row in still water?
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Renee rows a boat downstream for 27 miles. The return trip upstream took 24 hours longer.
If the current flows at 4 mph, how fast does Renee row in still water?
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Let "u" be Renee's boat speed in still water, in mph.
Then the effective speed downstream is  (u + 4)  mph  (the speed relative to the river's bank).

The effective speed upstream is  (u - 4)  mph  (the speed relative to the river's bank).

The time spent moving downstream is  27%2F%28u%2B4%29 hours.

The time spent moving   upstream is  27%2F%28u-4%29 hours.

The condition says that

27%2F%28u-4%29 - 27%2F%28u%2B4%29 = 24.

To solve this equation, multiply both sides by (u-4)*(u+4). You will get

27*(u+4) - 27*(u-4) = 24*(u-4)*(u+4).

Simplify

27u+%2B+108+-+27u+%2B+108 = 24%2A%28u%5E2+-+16%29,

216 = 24u%5E2+-+384,

24u%5E2 = 216+%2B+384,

24u%5E2 = 600,

u%5E2 = 600%2F24 = 25,

u = sqrt%2825%29 = 5 mph.

Answer. Renee's boat speed in still water is  5  mph.

Check.  Time downstream 27%2F%285%2B4%29 =  3 h.  Time upstream   27%2F%285-4%29 = 27 h.  Time difference 27 h - 3 h = 24 h.