SOLUTION: A bakery owner hires a new assistant to decorate doughnuts. The owner can decorate the day's supply four times as quickly as the assistant. Working together, they can decorate all
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Question 1190679: A bakery owner hires a new assistant to decorate doughnuts. The owner can decorate the day's supply four times as quickly as the assistant. Working together, they can decorate all the doughnuts in 32 minutes. How long would it take each to decorate the doughnuts, working individually? Answer by greenestamps(13200) (Show Source):
The owner works 4 times as fast as his assistant, so when working together he does 4/5 of the work.
Working together, they take 32 minutes to do the job.
So the owner does 4/5 of the job in 32 minutes and the assistant does 1/5.
The owner does 4/5 of the job in 32 minutes, so the number of minutes it would take him to do the job alone is 32/(4/5) = 32*(5/4) = 40.
The assistant does 1/5 of the job in 32 minutes, so the number of minutes it would take him to do the job alone is 32*5=160.
ANSWERS:
owner 40 minutes
assistant 160 minutes
Formally...
x = minutes the owner takes to do the job
4x = minutes the assistant takes to do the job
32 = minutes it takes them together to do the job
1/x = fraction of the job the owner does in 1 minute
1/(4x) = fraction the assistant does in 1 minute
1/32 = fraction they do together in 1 minute
multiply by 32x to clear fractions:
ANSWERS:
time for owner to do the job alone: x = 40 minutes
time for assistant to do the job alone: 4x = 160 minutes
