A problem on men and work

burgess

Help required to solve algebra 2 homework

A can do a piece of work in 5 days, but with the help of B,A can do it in 3 days. In how much time B alone can complete the same piece of work ?

Thanks

soroban

Math Team
Hello, burgess!

$A$ can do a piece of work in 5 days,
but with the help of $B$, $A$ can do it in 3 days.
In how much time can $B$ alone complete the same piece of work?

$A$ does the job in 5 days.
$\quad$In one day, $A$ does $\tfrac{1}{5}$ of the job.

$B$ does the job in $b$ days.
$\quad$In one day, $B$ does $\tfrac{1}{b}$ of the job.

In one day, working together, they can do $\tfrac{1}{5} + \tfrac{1}{b}$ of the job.

We are told that, working together, they can do the job in 3 days.
That is, in one day, working together, they can do $\tfrac{1}{3}$ of the job.

There is our equation! . . . $\dfrac{1}{5} + \dfrac{1}{b} \;=\;\dfrac{1}{3}$

Solve for $b$.