If a man and a boy can finish working in 26 hours...?

Question

If a man and a boy can finish working(together) in 26 hours, and the man works 6 hours, how long will it take for the boy to finish working?

Answer 1

Let "X" be the rate at which the man can do work, and "y" be the rate at which the boy can do work. Their combined rate gets the job done (1 unit of work) in 26 hours, so

(1 unit of work) / (X + y) = 26 hours
1 unit of work = (26 hours) * (X + y)

If the man works alone for 6 hours, he does an amount of work equal to
6 hours * X

So, the amount of work left to do is 1 unit, minus what the man finished:

work remaining = (1 unit of work) - (6 hours * X)
work remaining = (26 hours) * (X + y) - (6 hours * X)
work remaining = (26 hours * X) + (26 hours * y) - (6 hours * X)
work remaining = (20 hours * X) + (26 hours * y)

The amount of time it will take the boy to finish this amount of work is

time = work remaining / y
time = ((20 hours * X) + (26 hours * y)) / y
time = (20 hours * X) / y + (26 hours * y) / y
time = (20 hours * X/y) + 26 hours

So, the amount of time it takes for the boy to complete the remainder of the job depends on the ratio of man's work speed to the boy's. You didn't provide this information, so the question cannot be answered.

Answer 2

20 hours

Answer 3

If the man works 6h and the total hours are 26h then the kid wokrs 20 h
MAN + KID = 26h
6h + ? = 26h
? = 26h - 6h
? = 20h.