Problem Solving

LUANDATO wrote:Al can complete a particular job in 8 hours. Boris can complete the same job in 5 hours. Cody can complete a second job, which requires twice as much work as the first, in 8 hours. If all three people work together on the larger job 2 hours, how long, in hours, would it take Al, working alone, to finish the job?

A. 0.8
B. 3.0
C. 6.8
D. 8.0
E. 8.8

The OA is C.

I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

Job 1 rates:

Al: 1/8 job per hour
Boris: 1/5 job per hour
Cody: 1/4 job per hour (we know this because Cody can do a job that is twice as much work in 8 hours, thus he must be able to do Job 1 in 4 hours)

Job 2 rates (we know that Job 2 takes twice as long as Job 1):
Al: 1/16 job per hour
Boris: 1/10 job per hour
Cody: 1/8 job per hour

What is the larger job? This is Job 2 (it takes twice as long).

If Al, Boris and Cody work together for two hours on Job 2, how much is done? Well that is 2(1/16) + 2(1/10) + 2(1/8) = 1/8 + 1/5 + 1/4 = 5/40 + 8/40 + 10/40 = 23/40

Thus, 17/40 of the job remains to be completed after two hours. It will take Al 16 hours to do a full Job 2 so it will take him 16*(17/40) to do the remainder.

16*(17/40) = 4*17/10 = 68/10 = 6.8

Answer is C.