A craftsman and his apprentice working together can complete a project in 4 days. If each works on the project individually

project-individually

#1

A craftsman and his apprentice working together can complete a project in 4 days. If each works on the project individually, the apprentice would have taken 6 days more than the craftsman. How long would it take for the apprentice to do the job alone?

Answer:
12 days

If craftsman alone can complete the job in ‘x’ days, then apprentice alone will take x+6 days to complete the job.
As 1 day work of craftsman and apprentice=1/4, So (1/x)+[1/(x+6)] =1/4
(x+6+x)/ [x(x+6)] =1/4
x^2 - 2x -24=0
x^2-6x+4x-24=0
(x+4)(x-6)=0
x=6
So apprentice alone will take x+6 =6+6=12 days to complete the job.