SOLUTION: boat traveled 12 feet going south and 50 going west, totaling 62 feet in 16 seconds. heading south the boat traveled an average speed 3 feet per second less than its speed heading

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Question 1114961: boat traveled 12 feet going south and 50 going west, totaling 62 feet in 16 seconds. heading south the boat traveled an average speed 3 feet per second less than its speed heading west what was the speed of the boat heading west?
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52873) (Show Source):
You can put this solution on YOUR website!
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Let "w" be the boat speed heading west, in ft/s Then the speed going south is (w-3) ft/s. The time equation is + = 16. (*) It is the time equation, because each fraction in the left side is the time spent to travel the corresponding distance. The equation itself is the direct translation of the condition to Math. The solution is w = 5 ft/s. I got it mentally. You can solve the equation (*) multiplying both sides by w*(w-3). Check. Time going west = 10 seconds. Time going south = = 6 seconds. Total time 10 + 6 = 16 seconds. ! Correct !

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
boat traveled 12 feet going south and 50 going west, totaling 62 feet in 16 seconds. heading south the boat traveled an average speed 3 feet per second less than its speed heading west what was the speed of the boat heading west?
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south dist = 12 ft ; rate = r-3 ft/sec ; time = 12/(r-3) sec
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west dist = 50 ft ; rate = r ft/sec ; time = 50/r sec
Equation:
time + time = 16 seconds
12/(r-3) + 50/r = 16
12r + 50(r-3) = 16r(r-3)
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16r^2-48r = 12r + 50r-150
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16r^2 - 110r + 150 = 0
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8r^2 - 55r + 75 = 0
(r-5)(8r-15) = 0
r = 5 ft/sec (speed going south)
r-3 = 2 ft/sec (speed going west)
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Cheers,
Stan H.
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