Question

Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 3 hours. Working alone, it takes the slower worker 8 hours longer to do the job than the faster worker. How long does it take each to do the job alone?

Answer 1

Answer:

Faster worker takes 4 hours and slower worker takes 12 hours.

Step-by-step explanation:

Let x be the time ( in hours ) taken by faster worker,

So, according to the question,

Time taken by slower worker = (x+8) hours,

Thus, the one day work of faster worker = $\frac{1}{x}$

Also, the one day work of slower worker = $\frac{1}{x+8}$

So, the total one day work when they work together = $\frac{1}{x}+\frac{1}{x+8}$

Given,

They take 3 hours in working together,

So, their combined one day work = $\frac{1}{3}$

$\implies \frac{1}{x}+\frac{1}{x+8}=\frac{1}{3}$

$\frac{x+8+x}{x^2+8x}=\frac{1}{3}$  ( Adding fractions )

$3(2x+8)=x^2+8x$    ( Cross multiplication )

$6x+24=x^2+8x$       ( Distributive property )

$x^2+2x-24=0$          ( Subtraction property of equality )

By quadratic formula,

$x=\frac{-2\pm \sqrt{100}}{2}$

$x=\frac{-2\pm 10}{2}$

$\implies x=4\text{ or }x=-6$

Since, hours can not negative,

Hence, time taken by faster worker = x hours = 4 hours,

And, the time taken by slower worker = x + 8 = 12 hours.