Question

An office has two envelope stuffing machines. Working together they can stuff a batch of envelopes in $2$ hours. Working separately it will take the second machine $1$ hour longer than the first machine to stuff a batch of envelopes. How long would it take second machine to stuff a batch of envelopes by themselves?

• A. $4.5616$ hrs
• B. $3.5616$ hrs
• C. $5.5616$ hrs
• D. None of these

Answer 1

The correct option is A $4.5616$ hrs

Let the time taken by one machine to stuff a batch be $x$ hours.
Therefore the time taken by the second machine = $(x+1)$ hours
Two envelope stuffing machines working together = $2$ hours
So, $\frac{1}{x}+\frac{1}{x+1}=\frac{1}{2}$
$\frac{2x+1}{x^2+x}=\frac{1}{2}$

$4x+2=x^2+x$

$x^2-3x-2=0$

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{3\pm \sqrt{(-3{)}^2-4\times 1\times -2}}{2\times 1}$

$\frac{3\pm \sqrt{17}}{2}$

$\frac{3\pm 4.123}{2}$

So, $x=3.5616,x=-0.561$

Hence $x=3.5616$ since $x$ cannot be negative.

The second machine to stuff a batch of envelopes by themselves $=3.5616+1=4.5616$ hours.