Question

Mr. Itol's assistant takes twice as long to complete a computer task as Mr. Itol. If it takes both experts 6 hours to complete the task, how long will it take each of them to do the job alone?

Answer 1

So, in order to solve this problem, I will set up an equation. First, let's make x= the # of hours it takes Mr. Itol to complete a computer task, and since his assistant takes twice as long, lets make 2x=the # of hours it takes the assistant to complete the task. We also know that it takes the two of them 6 hours to complete the task together. We can now set up the following equation: 

$\frac{1}{2x} + \frac{1}{x} = \frac{1}{6}$

Now, in order to be able to solve this, we have to find the least common denominator, and then we can cancel out the denominators to solve for the top part. The LCD=6x and the new equation becomes: 

$\frac{3}{6x} + \frac{6}{6x} = \frac{x}{6x}$

Now, we can get rid of the denominators, and we get:

$3+6=x$

So, x= 9

Now we know that Mr. Itol would take 9 hours to complete the task if he were to do it himself. To find how long it would take his assistant to complete the same task by himself, we just need to plug in the x-value into 2x:

$2(9)=18$

Therefore, your answer is that Mr. Itol would take 9 hours to do the job alone, while his assistant will take 18 hours (double the time) to do the job alone.

Hope this helps :)