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 day, find the time taken by B to finish the work.
[4 MARKS]

Answer 1

Framing the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Suppose B alone can takes $x$ days to finish the work.

Then A alone can finish it in $(x-6)$ days.

B's 1 day's work = $\frac{1}{x}$.

A's 1 day's work = $\frac{1}{x-6}$.

(A+B)'s 1 day's work = $\frac{1}{4}$

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

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

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

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

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

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

$\Rightarrow x=12orx=2$

But $x$ cannot be less than 6.

$\Rightarrow x=12$

Hence, B alone can finish the work in 12 days