Question 208954: 3. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
The speed of a current is 6 mph. If a boat travels 62 miles downstream in the same time that it takes to travel 31 miles upstream, what is the speed of the boat in still water?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
The speed of a current is 6 mph. If a boat travels 62 miles downstream in the same time that it takes to travel 31 miles upstream, what is the speed of the boat in still water?
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Downstream DATA:
distance = 62 miles ; rate = b+6 ; time = 62/(b+6) hrs
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Upstream DATA:
distance = 31 miles ; rate = b-6 ; time = 31/(b-6) hrs
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Equation:
time down = time up
62/(b+6) = 31/(b-6)
Cross-multiply to get:
62(b-6) = 31(b+6)
62b - 6*62 = 31b + 31*6
31b = (31+62)6
b = 18 mph (speed of the boat in still water)
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Cheers,
Stan H.
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