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Question 255326: A boat traveled 45km downstream in 3 hours. The return trip against the current took 5 hours. Find the rate of the boat in calm water and the rate of the current.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! b = speed of the boat in calm water
c = speed of the current flowing downstream
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The typical distance equation is: d = rt, where
d = distance
r = rate
t = time
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Given d = rt, we can rearrange the equation as may be needed:
r = d/t
t = d/r
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We are told that the distance is 45 km.
d = 45 km
We are told the downstream time is 3 hr.
t = 3 hr
So,
45 = r*3
Dividing both sides by 3:
15 = r
r = 15 km/hr.
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The downstream rate will be the speed of the boat plus the speed of the current: b+c.
(b+c) = 15 km/hr
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We also are told the return time upstream was 5 hr.
45 = r*5
Dividing both sides by 5:
9 = r
r = 9 km/hr
The upstream rate will be the speed of the boat minus the speed of the current: b-c.
(b-c) = 9 km/hr
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Now we have two linear equations:
b + c = 15
b - c = 9
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Adding them we have:
2b = 24
Dividing both sides by 2
b = 12
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Substitute b=12 into the downstream equation to find 'c':
12 + c = 15
c = 3
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Check by substituting into the upstream equation:
12 -3 = 9. True.
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So, the rate of the boat in calm water is 12 km/hr, and the rate of the current is 3 km/hr.
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Done.
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