Travel by boat Alonzo can travel from his camp downstream to

Travel by boat. Alonzo can travel from his camp downstream to the mouth of the river in 30 minutes. If it takes him 45 minutes to come back, then how long would it take him to go that same distance in the lake with no current?

Solution

Downstream DATA:
Time = (1/2) hr. ; distance = x miles ; rate = x/(1/2) = 2x mph
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Upstream DATA:
Time = (3/4) hr. ; distance = x miles : rate = x/(3/4) = (4x/3) mph
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Equations:
b + c = 2x
b - c = (4x/3)
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Add to get:
2b = (10x/3)
b = (5x/3) speed of the boat in still water
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Substitute into b+c = 2x to solve for \"c\":
(5x/3) + c = 2x
c = x/3 (speed of the current)
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how long would it take him to go that same distance in the lake with no current?
Ans: d/b = x/(5x/3) = 3/5 hr = 36 minutes