algebra precalculus - Time and Work ::

A and B can do a work in 5 days B and C can do a work in 4 Days.A start the Work and leave after 4 Days Then B joined and left after 3 days .Remaining work done by C in how many Days

I Have tried:

A and B can do a piece of work in 1 Day is 1/5

similarly B and C is 1/4

After that I am not able to proceed with this sum, Please anyone guide me for the Answer

Answer

Suppose $A,B,C$ does $1/x,1/y,1/z$ part of the in $1$ day. Then

$1/x+1/y=1/5$ and $1/y+1/z = 1/4$.

Let $C$ work for $d$ days. Then by problem $4/x+3/y+d/z=1$.

Now find the value of $d$ using the constraints.