Question 248519
We start with what we know about distance problems.
d = r * t, where d=distance, r=rate, and t=time
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Upstream info:
60=r*5
r = 12 mph
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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.
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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.
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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.
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Downstream:
D = X + C
In English, the downstream rate = max speed of the boat PLUS the current pushing it along.
X+C=20
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So we have two equations and two unknowns. Piece of cake.  Right?
X - C = 12
X + C = 20
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Let's add them.
2X = 32
X = 16
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So the unknown maximum speed X is 16.
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Now we check our work, as we always do...
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Looking back at what we know,
X-C = 12
16-C=12
C=4
OK
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And we know
X+C = 20
16 + C = 20
C=4
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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.