How long would it take one man to do it alone

A man and a boy can do in 15 days a piece of work which would be done by 7 men and 9 boys in two days.

http://www.imagecross.com/a/image-hostin…

Let m = fraction of job done by 1 man in 1 day
Let b = fraction of job done by 1 boy in 1 day

15m + 15b = 1 job
14m + 18b = 1 job

210m + 210 b = 14 jobs
210m + 270 b = 15 jobs
60 b = 1 job

boy alone would take 60 days

15m + 15/60 = 1 job
15m = 45/60 = 3/4 job
m = 3 / 60 = 1/20 job

1 man working alone would take 20 days.

Checking:

1 man + 1 boy for 15 days =
15 * 1/20 + 15 * 1/60 = 3/4 + 1/4 = 1 job

7 men + 9 boys for 1 day =
7 * 1/20 + 9 * 1/60 = (21 + 9) / 60 = 30 / 60 = 1/2 job
* 2 for second day = 1 job


Alternate method for solving the equations:
15m + 15b = 1 job
14m + 18b = 1 job

Subtract:
3b - m = 0
3b = m
Substitute:
45b + 15b = 1 job
b = 1/60
m = 1/20
That's a little quicker.