MHB Solve Work Rate Problem: Find A and B's Time Alone

[Drain Brain]

I just want an alternative solution(preferably easier approach) to this problem

"A" can finish a job two hours longer than "B". After working for 1 hour, "B" joins him and they complete the job in 3 more hours. How long would it take "A" and "B" to finish a similar job if each worked alone?

my solution,

Let $B+2=$ A's required time to finish the job alone
$B=$ B's required time to finish the job alone

$\frac{1}{B+2}+3\left(\frac{1}{B+2}+\frac{1}{B}\right)=1$

solving for B I have

$B=6$hours
$A=8$hours

Regards!:)

 

[Ackbach]

Well, I don't think there could be a much simpler way to solve this problem. You've got to work with times and rates like you're doing. There are two unknowns, which means you'd have to have two equations.