Question

WORD PROBLEM

Answer 1

The complete question: Working together it takes two computers 10 minutes to send out a company’s email. If it takes the slower computer 35 minuets to do the job on its own, how long will it take the faster computer to do its job on its own ?

To solve this, we are going to use the formula for rate of work problems: $\frac{1}{T_{a}} + \frac{1}{T_{b}} = \frac{1}{T_{t} }$
where
$T_{a}$ is the time it takes the first worker (person or machine) to complete the job.
$T_{b}$ is the time it takes the second worker (person or machine) to complete the job.
$T_{t}$ it the tames it takes to both workers working together to complete the job.

Let $T_{b}$ be the it takes the slower computer to the job, so $T_{a}$ will be the time it takes the faster computer to do the job. We know from our problem that it takes the slower computer 35 minuets to do the job on its own, so $T_{b}=35$; we also know that it takes 10 minutes to both computers working together to do the job, so $T_{t}=10$. Lets replace those values in our formula to find $T_{a}$:
$\frac{1}{T_{a}} + \frac{1}{T_{b}} = \frac{1}{T_{t} }$
$\frac{1}{T_{a}} + \frac{1}{35} = \frac{1}{10 }$
$\frac{1}{T_{a} } = \frac{1}{10} - \frac{1}{35}$
$\frac{1}{T_{a} } = \frac{1}{14}$
$T_{a}=14$

We can conclude that it takes the faster computer 14 minutes to do the job on its own.