SOLUTION: It takes 10 hours for a bakery owner to finish the orders for Christmas. After he worked for 4 hours, his wife came to help him. He completed the orders with her help in another 4

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Question 978601: It takes 10 hours for a bakery owner to finish the orders for Christmas. After he worked for 4 hours, his wife came to help him. He completed the orders with her help in another 4 hours. How long would it have taken if his wife had done the orders by herself?
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
"The orders for christmas" is one job. The wife's rate is unknown, r.

The owner's rate is 1%2F10 jobs per hour.
The job is split into two parts of 4 hours each.

Instead of r, use 1/x for the wife's rate.

%281%2F10%29%2A4%2B%281%2Fx%2B1%2F10%29%2A4=1, the two parts of the job, four hours just the owner and four more hours both wife and owner, all to do the ONE job. Solve the equation for x.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
He worked 4 hours leaving 6 more hours for him.
rate for A alone 6 baker
rate for A & B together 4
1/a+1/b=1/x
1/6+1/b=1/4
1/b=1/4-1/6
1/b=6/24-4/24
1/b=2/24
1/b=1/12
b=12
rate for wife alone 12 hours for the remaining 6 hours
check
1/6+1/12=1/4
12/72+6/72=1/4
18/72=1/4
ok
codewa
But we want to know how long it would have taken her for the whole job not just part of it
he works twice as fast as she does so the job that takes him 10 hours alone would take her 20 hours alone.