How long will it take the older daughter to do the job by herself?

Question

a woman can do a certain job in 10 hr and her younger daughter can do it in 12 hr. after the woman and her younger daughter have been working for 1 hr they are joined by the older daughter, and the three completed the job in 3 more hr. how long will it take the older daughter to do the job by herself?

Answer 1

The woman can do 1/10 of the job in an hour.

The younger daughter can do 1/12 of the job in an hour.

After 1 hour they will have done 1/10 + 1/12 of the job

1/10 + 1/12

= 6/60 + 5/60

= 11/60

That leaves 49/60 of the job to be done by all 3.

Let's assume it take the older daughter X hours to do the job alone.  So she will contribute 1/X of the job completion per hour.  Remember it takes them 3 hours, so multiply by 3:

Remaining job:

3(1/10 + 1/12 + 1/X) = 49/60

3/10 + 1/4 + 3/X = 49/60

Multiply by 60 to remove fractions:

18 + 15 + 180/X = 49

33 + 180/X = 49

180/X = 16

16X = 180

X = 180/16

X = 11.25

The older daughter would take 11 1/4 hours to do the job alone.

Answer 2

Woman = 1/10 per hour

Daughter = 1/12 per hour

Older daughter = x

After one hour, 11/60 of job has been done

3(1/10 + 1/12 + x) = 49/60 of job

33/60 + 3x = 49/60 of job

3x = 16/60 of job

x= 4/45 of job in one hour

The older daughter could complete the job in 45/4 hours or 11 1/4 hours