SOLUTION: Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will j
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Question 210711: Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will john complete the work? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will john complete the work?
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John DATA:
time = x day/job ; rate = 1/x job/day
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Sam DATA:
time = x-6 days/job ; rate = 1/(x-6) job/day
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Together DATA:
time = 4 days/job ; rate = 1/4 job/day
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Equation:
rate + rate = together rate
1/x + 1/(x-6) = 1/4
4(x-6) + 4x = x(x-6)
4x - 24 + 4x = x^2 - 6x
x^2 - 14x +24 = 0
x^2 - 12x - 2x + 24 = 0
x(x-12)-2(x-12) = 0
(x-12)(x-2) = 0
To get a positive solution for Sam and John:
x = 12 days (John time)
x-6 = 6 days (Sam time)
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Cheers,
Stan H.
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