2 pipes running together can fill a cistern in 3 1:3 min. if one pipe takes 3 min more than the other to fill it, find the time in which each pipe would fill the cistern

It takes one pipe x minutes, the other pipe x+3 minutes

the portion filled per minute is by one pipe is 1/x, by the second pipe 1 / (x+3)

when two pipes running together:

3&1/3[1/x+1 / (x+3) ] = 1, 1 means the whole cistern

solve for x: 3&1/3 (x+3) + 3 1/3 (x) = x (x+3)

6 &2/3 x + 10 = x^2+3x

x^2 - (3&2/3) x-10=0

3x^2-11x-30=0

this cannot be factored, so use the quadratic equation:

x is about 5.5

x+3=8.5