# Math Help - work problem

1. ## work problem

A is twice as good a workman as B and together they finish a piece of work in 18 days.in how many days will A alone finish this work?

2. Originally Posted by neha1
A is twice as good a workman as B and together they finish a piece of work in 18 days.in how many days will A alone finish this work?
Lets suppose that worker A works finishes a job in A days

and worker B finishes a job in B days

Then worker A's rate is $\frac{1}{A}$

Then worker B's rate is $\frac{1}{B}$

But we know that worker A is "twice" as good (2 times as fast) as worker B

so $\frac{1}{A}=2\cdot \frac{1}{B}$

We can now set the rates equal

$\frac{1}{A}+\frac{1}{B}=\frac{1}{18}$

$2\cdot \frac{1}{B}+\frac{1}{B}=\frac{1}{18}$

$\frac{3}{B}=\frac{1}{18} \iff 54=B$

Plugging in and solving for A gives A=27.

I hope this helps