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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 hours.
The time spent moving upstream is hours.
The condition says that
- = 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
= ,
= ,
= ,
= ,
= = ,
u = = 5 mph.
Answer. Renee's boat speed in still water is 5 mph.
Check. Time downstream = 3 h. Time upstream = 27 h. Time difference 27 h - 3 h = 24 h.