Question 248519: Please help me help my son with this word problem ...
A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water? What is the rate of the current?
Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A boat travels 60 km upstream (against the current) in 5 hours.
Upstream DATA:
distance = 60 km ; time = 5 hrs ; rate = distance/time = 60/5 = 12 mph
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The boat travels the same distance downstream in 3 hours.
Downstream DATA:
distance = 60 km ; time = 3 hrs ; rate = d/t = 60/3 = 20 mph
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What is the rate of the boat in still water?
What is the rate of the current?
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Let the rate of the boat in still water be "b"
Let the rate of the current be "c".
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Equations:
b + c = 20 mph
b - c = 12 mph
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Add the equation and solve for "b":
2b = 32
b = 16 mph (rate of the boat in still water)
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Substitute b=16 into b+c = 20 to solve for "c":
16 + c = 20
c = 4 mph (rate of the current)
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Cheers,
Stan H.
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! We start with what we know about distance problems.
d = r * t, where d=distance, r=rate, and t=time
.
Upstream info:
60=r*5
r = 12 mph
.
Downstream
60 = r*3
r = 20
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We need to assume the boat runs as fast as possible in both directions, otherwise we cannot solve the problem.
.
Let's call the upstream rate: U
Let's call the downstream rate: D
Let's call the unknown maximum rate: X
And finally, the current is flowing at C mph.
.
Upstream:
U = X-C
In English, the upstream rate = max speed of the boat MINUS the current flowing against it.;
X - C = 12, as shown above.
.
Downstream:
D = X + C
In English, the downstream rate = max speed of the boat PLUS the current pushing it along.
X+C=20
.
So we have two equations and two unknowns. Piece of cake. Right?
X - C = 12
X + C = 20
.
Let's add them.
2X = 32
X = 16
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So the unknown maximum speed X is 16.
.
Now we check our work, as we always do...
.
Looking back at what we know,
X-C = 12
16-C=12
C=4
OK
.
And we know
X+C = 20
16 + C = 20
C=4
.
Checking the upstream rate...
60/(16-4)= 60/12 = 5, which is how long we were told it took.
Checking the downstream rate...
60/(16+4) = 60/20 = 3, which is how long we were told it took.
Done.
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