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Question 455185: Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 1o min. If the current in that part of the river is 3 km per hour, what was her boat speed in still water?
Can someone show me the set up for this?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 1o min. If the current in that part of the river is 3 km per hour, what was her boat speed in still water?
Can someone show me the set up for this?
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Upstream DATA:
time = 1/2 hr ; distance = x km ; rate = d/t = x/(1/2) = (2x) km/h
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Downstream DATA:
time = 1/6 hr ; distance = x km ; rate = d/t = x/(1/6) = (6x) km/h
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Upstream rate = b-3 km/h where b is the speed of the boat in still water
Downstream rate b+3 km/h
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Solve this system of equations:
rate = rate:
b-3 = (2x)
b+3 = (6x)
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Subtract and solve for "x":
6 = 4x
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x = 3/2 km
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Solve for "b":
b -3 = 2x
b -3 = 2(3/2)
b -3 = 3
b = 6 km/h (speed of the boat in still water)
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A shorter way to work the problem.
Let b+3 be downstream rate.
and b-3 be upstream rate.
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Distance up = Distance down = (rate)(time)
(b+3)(1/6 hr) = (b-3)(1/2 hr)
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Multiply both sides by 12 to get:
2b+6 = 6b-18
4b = 24
b = 6 km/hr (speed of the boat in still water)
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Cheers,
Stan H.
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