You estimate that you can do 12 math problems in 45 minutes. How long should it take you to do 20 math problems?

For this problem, we can set up a system of inequalities. It takes 45 minutes to do 12 math problems, so we can set up a fraction as 45/12.

The ratio of minutes to problems doesn't change, so we can set this fraction as equal to what we are searching for. We are looking for the time it takes to do 20 problems, so we can put x over 20 to find the number of problems completed.

Now we can set up the equation.

45/12=x/20

We have the equation, so we just have to solve for x to find the time required to do 20 math problems.

45/12=x/20

20 (45/12) = x

x=75 minutes

It takes 75 minutes to complete 20 math problems.