Algebra 2

From the question, we know that it takes 9 hours for Sam & Albert to finish the fence. Thus, the rate of them painting is 1/9th per hour.

We also know that Sam and Albert spent 4 hours painting, or another way to put it, they completed 4/9th of the fence. Thus, 5/9th remains unfinished. Then came along John. The 3 took 2 hours to complete 5/9th of the fence. Thus, the 3 can paint 5/18th per hour.

Previously, we calculated that it takes Sam and Albert an hour to paint 1/9th. With the three, the rate has gone up to 5/18th an hour. Hence, John's contribution is 5/18-1/9 =3/18th per hour.

Therefore, if John would to paint this fence ALONE, and at the rate of 3/18th per hour, it will take him 18/18 * 18/3 hour to complete or 6 hours.

Without John, Sam and Albert would take 4+5 =9 hours. So for 4 hours, they have done 4/9th of the job with 5/9 to go. If the three can take 2 hours to complete 5/9 of the job, in 1 hour, they will cover 5/18. We already established that Sam and Albert would take 1 hour to complete 1/9. John alone, he would complete 5/18 - 1/9 = 3/18 of the job in an hour. So he would take 1/(3/18) = 18/3 = 6 hours alone.

(Each name is 1 man hour for that particular person)

For the finished job: 6(sam +albert) + 2(John) or 9(sam + albert)

Hence 2(john) = 3(sam +albert)

Hence it requires 3*2(john) => 6 hours of john working