A can do a piece of work in 2/3 as many days as B, and B can do the same work in 4/5 as many days as C. Together they can do the work in 3 7/11 days. In how many days can A do the work alone?
Suppose C can do one complete job in x days.
Then C's work rate in jobs per day is
B can do the same work in 4/5 as many days as C
So B can do the job in days.
Then B's work rate in jobs per day is
Simplify that compound fraction by multiplying top and bottom by 5
So B's work rate is
A can do a piece of work in 2/3 as many days as B
Since B can do the job in days,
A can do the job in days.
So A can do the job in days
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Then A's work rate in jobs per day is
Simplify that compound fraction by multiplying top and bottom by 15
So A's work rate is
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Together they can do the work in 3 7/11 days.
Change to improper fraction
Then all three's combine work rate in jobs per day is
Simplify that compound fraction by multiplying top and bottom by 11
So their combined work rate is
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The equation comes from:
Multiply through by the LCD of :
So C can finish the job in 15 days.
The qustion is:
In how many days can A do the work alone?
A can do the job in days, or
or 8 days. That's the answer.
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To check we need how many days it takes B to do the job alone:
B can do the job in days.
That's or 12 days.
To check, add their rates in jobs per day to see if we get
That checks, so we are right.
A can complete the job in 8 days.
Edwin