Question

An experienced employee can enter tax data into a computer tree times as fast as a new employee. Working together, it takes them 9hrs. How long would it take the experienced employee working alone?

Answer 1

Answer:

12 hours

Step-by-step explanation:

Let x hours be the time needed for the experienced employee, then 3x hours is time needed for the new employee.

Then, the experienced employee completes $\dfrac{1}{x}$ of the whole work per hour and the new employee completes $\dfrac{1}{3x}$ of the whole work per hour.

Altogether the can complete

$\dfrac{1}{x}+\dfrac{1}{3x}=\dfrac{4}{3x}$

of the whole work per hour and need

$\dfrac{1}{\frac{4}{3x}}=\dfrac{3x}{4}$

hours to finish the whole work.

Working together, it takes them 9 hours, then

$\dfrac{3x}{4}=9\\ \\3x=36\\ \\x=12\ hours$