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

To solve this, we are going to use the work-rate formula: 
where
is the time the teacher takes to grade the homework papers
is the time the assistant takes to grade the homework papaers
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 . We also know that If the teacher helps the grading can be completed in 20 minutes, so . Lets replace those values in our formula: 






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

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

there is a hike in both the graphs so the graphs are increasing on their domain.x-intercept of log x and log 6x are differentthere is a vertical asymptote of both the graphs so there is no y-interceptas both the graphs are increasing so there is no horizontal asymptote