Question

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days the the fraction of the work that is left is

Answer 1

We have work, call it W. Find their power, or how quickly they can accomplish this work:

$$P_1=\frac W{15},\space P_2=\frac W{20}.$$

Powers can be simply added together, so, calculate the work they both accomplish if help each other during T=4 days:

$$W_1=TP=4(P_1+P_2)=4\bigg(\frac W{15}+\frac W{20}\bigg)=\frac{7W}{60}.$$

What left is

$$k=\frac{W-W_1}{W}=\frac{W-4\cdot\frac{7W}{60}}{W}=\frac8{15}.$$