Question

The teachers assistant and grade homework papers by herself in one hour. If the teacher helps the grading can be completed in 20 minutes. how long will it take the teacher to grade the papers working alone?

Answer 1

To solve this, we are going to use the work-rate formula: $\frac{1}{t_{1} } + \frac{1}{t_{2}} = \frac{1}{t}$
where
$t_{1}$ is the time the teacher takes to grade the homework papers
$t_{2}$ is the time the assistant takes to grade the homework papaers
$t$ is the tame they take to grade the homework papers working together

Remember that there are 60 minutes in in hour, so 1 hour equals 60 minutes; therefore $t_{2}=60$. We also know that If the teacher helps the grading can be completed in 20 minutes, so $t=20$. Lets replace those values in our formula: 
$\frac{1}{t_{1} } + \frac{1}{t_{2}} = \frac{1}{t}$
$\frac{1}{t_{1} } + \frac{1}{60} = \frac{1}{20}$
$\frac{1}{t_{1} } = \frac{1}{20} - \frac{1}{60}$
$\frac{1}{t_{1} }= \frac{1}{30}$
$t_{1}=30$

We can conclude that the teacher will take 30 minutes to grade the homework papers.