Question 285932: Upstream, downstream. Junior’s boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! D = R*T, where D=distance, R=rate of speed, and T=time
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S = speed in calm water = 15
C = current speed
S-C = speed going upstream
S+C = speed going downstream
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T = D/R
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Upstream...
T = 9/(S-C)
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Downstream...
T = 12/S
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Transitive property lets us eliminate T...which is good since we don't know what T is...
9/(S-C) = 12/S
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Cross multiply...
9S = 12*(S-C) = 12S - 12C
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Substitute S=15...
9(15) = 12(15) - 12C
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135 = 180 - 15C
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Add 15C to both sides...
15C + 135 = 180
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Subtract 135 from both sides...
15C = 45
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Divide both sides by 15
C = 3 = current speed
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Checking the answer by checking the time up and downstream..
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T = 9/(S-C) = 9/9 = 1 hr
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T = 15/(S+C) = 15/(12+3) = 15/15 = 1 hr
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Correct.
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Answer:
The current is 3 mph.
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