SOLUTION: Mr. Housenecht can do a piece of work in two and a half days and Mr. Warwick in three and one-third days. In how many days can both do it.

Question 937609: Mr. Housenecht can do a piece of work in two and a half days and Mr. Warwick in three and one-third days. In how many days can both do it.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
rate is work over time:
r = w/t
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work can be anything such as 1 for one "job", or 1 for "a piece of work", or it can be a fraction or a multiple of a job, for example 0.75 of a job, or 3.83 jobs, etc.
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each man's rate:
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rate Housenecht:
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two and a half days = 2+1/2 = 2.5 days
rateHousenecht = w/t
rateHousenecht = 1/(2+1/2)
rateHousenecht = 1/2.5
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rate Warwick:
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three and one-third days = 3+1/3 = 3.333333333
rateWarwick = w/t
rateWarwick = 1/(3+1/3)
rateWarwick = 1/3.333333333
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the rates of the two men are additive:
r = rateHousenecht + rateWarwick
r = 1/2.5 + 1/3.333333333
r = 0.7
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t = w/r
t = 1/0.7
t = 1.42857142857
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answer:
together they can finish in about 1.43 days
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