Question 280810: A motorboat traveling with the current can go 36 miles in 2 hours. against the current it takes 3 hours to go to the same distance. Find the rate of the motorboat in calm water.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! d = r*t is the basic distance equation.
s = speed of the motor boat in calm water
c = speed of current
s + c = speed of the boat traveling with the current
s - c = speed of the boat traveling against the current
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traveling with the current the boat went 36 miles in 2 hrs
d = 36
r = s+c
t = 2
36 = (s+c)*2
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traveling against the current the boat can return 36 miles in 3 hrs
d = 36
r = s-c
t = 3
36 = (s-c)*3
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We've got two unknowns and we've got two unknowns, so this can be approached as a system of linear equations.
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2s + 2c = 36
3s - 3c = 36
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Multiply the first equation by 3 and the second by 2 to enable elimination.
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3(2s + 2c) = 3(36) = 6s + 6c = 108
2(2s - 2c) = 2(36) = 6s - 6c = 72
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6s + 6c = 108
6s - 6c = 72
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adding them to eliminate the 6c and -6c.
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12s = 180
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divide by 12
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s = 15 = speed of the boat in calm water
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substituting back into our first equation
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36 = (s+c)*2
2s + 2c = 36
2(15) + 2c = 36
2c = 6
c = 3 = speed of the current
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checking...
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traveling with the current, the boat's speed = 15+3 = 18
to travel 36 miles, it would take 2 hr, which is what the problem stated.
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traveling against the current, the boat's speed = 15 -3 = 12
again we can see that to travel the 36 miles it would take 3 hrs, which is also what was stated.
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Answer:
s = 15 = speed of the boat in calm water
c = 3 = speed of the current
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Done
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