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 t

Question

Liula

2 months ago

11

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 t

he task, how long will it take each of them to do the job alone?

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-02-26T04:18:37+03:00

To tackle this problem, I will formulate an equation. Let's designate x as the number of hours Mr. Itol requires to finish a computer task, while since his assistant needs twice as long, we'll set 2x as the hours the assistant needs. We also know that together they complete the task in 6 hours, allowing us to establish the following equation:

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

Now, to solve this, we need to identify the least common denominator, allowing us to eliminate the denominators. The LCD is 6x, which modifies our equation to:

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

Next, we can eliminate the denominators, resulting in:

$3+6=x$

Thus, x = 9.

This tells us that Mr. Itol would take 9 hours to work on the task alone. To calculate the duration needed for his assistant to complete it independently, we substitute the x-value into 2x:

$2(9)=18$

Consequently, the final determination is that Mr. Itol would need 9 hours to finish the task alone, while his assistant would require 18 hours (twice as long) to do so independently.

Hopefully, this is clear!:)