SOLUTION: A can do a piece of work in 7 days of 10 hours each & B can do it in 5 days of 12 hours each. How long will they take to do it, working together hours a day

Question 537125: A can do a piece of work in 7 days of 10 hours each & B can do it in 5 days of 12 hours each. How long will they take to do it, working together hours a day
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
Job problems are a lot like the D=RT problems. The formula is J=RT where J is the whole job, generally 1, while R is the rate of work and T is the time.

A completes the job in 7 days times 10 hours = 7 * 10 = 70 hours. So A's rate is 1/70 of the job per hour.

B completes the job in 5 days times 12 hours = 5 * 12 = 60 hours. So B's rate is 1/60 of the job per hour.

Working together they combine their rates. 1/60 + 1/70 = (60+70)/4200 = 130/4200 = 13/420.

1 = 13/420*T

That will give the time, in hours, it takes them to complete the job while working together. The question seems incomplete, because it says "working together hours a day." What is that blank? How many hours a day do they work together? Whatever it is, divide the answer we find (total hours) by whatever is in that blank to find the number of days.

Divide both sides by 13/420.

420/13 = T = 416 and 4/13 hours.

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