X does half as much work as Y in (1/3)rd of the time. If together they take 20 days to finish a job, how much days shall Y take to do it?

Shiva:

Let R

_{x}= The rate of work being performed by X and R_{y}= The rate of work being performed by Y. The work accomplished by each can be expressed as the rate * time of each.The total work accomplished by

**both**X and Y in 20 days can be expressed as the sum: W=R_{x}*20 + R_{y}*20Since we know that X accomplishes 1/2 the work in 1/3 the time of Y, Rx would correspond to a rate of ((1/2)/(1/3))Ry or (3/2)Ry

Substituting for Rx in the above equation for work, the total work accomplished by both X and Y in 20 days is: W=20(3/2) Ry+20 Ry = 30Ry+20 Ry = 50Ry

Let T

_{solo}represent the time to accomplish this same amount of work by Y alone. The total work (50Ry) is then equal to R_{y }times T_{solo:}_{ }50Ry=Ry*T_{solo}.Dividing both sides by R

_{y, }we obtain**T**_{solo}=50 days.Hope this helps!

George T.