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put this solution on YOUR website! Please help me solve this problem: A boat goes downstream a distance of 5 miles in 15 minutes, but it takes 20 minutes for the return trip. Find the right of the boat in still water and the rate of the current.
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First, convert all times given from minutes to hours.
20 mins * 1hr/60mins = 20/60 = 1/3 = .333 hours
15 mins * 1hr/60mins = 15/60 = 1/4 = .25 hours
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Let b = rate of the boat
and c = rate of the current
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we have two unknowns, so we'll need two equations.
We will need to apply the "distance formula":
d = rt
where
d is distance
r is rate
t is time
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from: "A boat goes downstream a distance of 5 miles in 15 minutes"
we get equation 1:
(b+c)(1/4) = 5
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from: "but it takes 20 minutes for the return trip"
we get equation 2:
(b-c)(1/3) = 5
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Solve equation 1 for c:
(b+c)(1/4) = 5
b+c = 20
c = 20-b
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Plug the result above into equation 2 and solve for b:
(b-c).333 = 5
(b-(20-b))(1/3) = 5
(b-20+b) = 15
2b-20 = 15
2b = 35
b = 17.5 mph (rate of boat)
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Plug the result above back into equation 1 and solve for c:
(b+c)(1/4) = 5
(17.5+c)(1/4) = 5
17.5+c = 20
c = 2.5 mph (rate of current)
