SOLUTION: Word problem. Ships. After a small oil spill, two cleanup ships are sent to siphon off the oil floating in Baffin Bay. The newer ship can clean up the entire spill by itself in 3

Question 526468: Word problem.
Ships. After a small oil spill, two cleanup ships are sent to siphon off the oil floating in Baffin Bay. The newer ship can clean up the entire spill by itself in 3 hours less time than the older ship takes by itself. Working together the two ships can clean up the oil spill in 8 hours. How long will it take the newer ship by itself to clean up the spill? Please explain how you get the answer. Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The newer ship can clean up the entire spill by itself in 3 hours less time than the older ship takes by itself. Working together the two ships can clean up the oil spill in 8 hours. How long will it take the newer ship by itself to clean up the spill?
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older ship time = x hrs/job ; rate = 1/x job/hr
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newer ship time = x-3 hrs/job ; rate = 1/(x-3) job/hr
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Together time = 8 hrs/job ; rate = 1/8 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x-3) = 1/8
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Multiply thru by 8x(x-3) to get:
8(x-3) + 8x = x(x-3)
16x-24 = x^2-3x
x^2-19x+24 = 0
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x = [19 +- sqrt(19^2-4*24)]/2
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x = [19 +- sqrt(265)]/2
x = [19 +- 16.28]/2
Reasonable solution:
x = 17.64 hrs (older ship time)
x-3 = 14.64 hrs (newer ship time)
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Cheers,
Stan H.
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