Question

A takes $6$ days less than the time taken by B to finish a piece of work. If both A and B together can finish it in $4$ days, find the time that B would take to finish this work by himself.

Answer 1

$\Rightarrow$ Let $B$ takes $x$ days to finish the piece of work.

$\Rightarrow$ Then, $A$ takes $x-6$ days to finish the piece of work.

Then, work done in one day,

$\Rightarrow$ $\frac{1}{x}+\frac{1}{x-6}=\frac{1}{4}$

$\Rightarrow$ $\frac{x-6}{x(x-6)}+\frac{x}{x(x-6)}=\frac{1}{4}$

$\Rightarrow$ $4(x-6+x)=x^2-6x$

$\Rightarrow$ $4(2x-6)=x^2-6x$

$\Rightarrow$ $8x-24=x^2-6x$

$\Rightarrow$ $x^2-14x+24=0$

$\Rightarrow$ $x^2-12x-2x+24=0$

$\Rightarrow$ $x(x-12)-2(x-12)=0$

$\Rightarrow$ $(x-12)(x-2)=0$

$\Rightarrow$ $x-12=0$ and $x-2=0$

$\therefore$ $x=12$ and $x=2$

$\Rightarrow$ If the time it takes $B$ is $2days$, then the times it takes $A$ is $-4$ days, which is not possible.

$\therefore$ The time that $B$ would take $12days$ to finish work by himself.