SOLUTION: A can do a job in 12hrs. B can do the same job in 16hrs. A does a part of work and leaves the rest for B. If A works for 9hrs, how many hours will it take B to finish the remaining

Question 239761: A can do a job in 12hrs. B can do the same job in 16hrs. A does a part of work and leaves the rest for B. If A works for 9hrs, how many hours will it take B to finish the remaining job?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A = rate of A = 1/12 of the job in 1 hour.
B = rate of B = 1/16 of the job in 1 hour.

A * (1/12) * 12 = 1 means A takes 12 hours to complete 1 job.

B * (1/16) * 16 = 1 means B takes 16 hous to complete 1 job.

A * 9 = (1/12)*9 = 9/12 means A completes 9/12 of the job in 9 hours.

1 - 9/12 = 3/12 means 3/12 of the job remains to be done.

B * x = 3/12 means B will complete 3/12 of the job in x hours.

x = (3/12) / B means divide both sides of the equation by B to solve for x.

x = (3/12) / (1/16) means dividing by B is the same as dividing by (1/16)

x = (3/12) * (16) means dividing by (1/16) is the same as multiplying by 16.

x = (3 * 16) / 12 means (3*16)/12 is equivalent to (3*16)/12.

x = 16 / 4 means simplify the expression.

x = 4 means solve for x to get the answer.

It will take B 4 more hours to complete the job.

That's a total of 9 + 4 = 13 hours.

9 * (1/12) + 4 * (1/16) = (9/12) + (1/4) = (3/4) + (1/4) = 1 means confirm the answer is good by carrying out the complete calculation with the solved value for x.

9/12J =

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