Two tailors, Danielle and Tammy, sit down to do some embroidery. Danielle can embroider 6 shirts per hour, and Tammy can get through 4 shirts per hour. In addition, the tailors had previously finished some shirts. Danielle has already completed 9 shirts, and Tammy has completed 11 shirts. Danielle and Tammy decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished? How long will that take?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?