25 women did 1/5 of job in 8 days. Then, because of an emergency, it became necessary to complete the job in the next 20 days. How many additional women needed to be added to the crew of 25 to accomplish this?
I'll show you two ways to do this:
25 women can do 1/5 of the job in 8 days. Therefore,
25 women can do the whole job in 40 days. Therefore,
50 women can do the whole job in 20 days. Therefore,
since only 4/5th of the job needs completing, it will
only take 4/5ths of 50 women to do the remaining 4/5ths
of the job, and 4/5ths of 50 is 40. They already have
25 women, so they'll need 40-25 or 15 more women.
Another way to do this is with the worker-time-job formula, which is:
where
W1 = the number of workers in the first situation.
T1 = the number of time units (days in this case) in the first situation.
J1 = the number of jobs (or fraction thereof) in the first situation.
W2 = the number of workers in the second situation.
T2 = the number of time units (days in this case) in the second situation.
J2 = the number of jobs (or fractionthereof) in the second situation.
W1 = 25 W2 = the unknown quantity
T1 = 8 T2 = 20
J1 = 1/5 J2 = 4/5
To divide by a fraction, invert it and multiply:
40 = W2
So it will take a total of 40 workers. There are already 25 workers,
so it will take 40-25 = 15 more workers.
Answer: 15 more workers.
Edwin