Jordan is a manager of a car dealership. he has two professional car washers, matthew and arianna, to clean the entire lot of cars. matthew can wash all the cars in 14 hours. arianna can wash all the cars in 11 hours. jordan wants to know how long it will take them to wash all the cars in the lot if they work together.

If we say there are 100 cars in a lot (It's an arbitrary number. You can use any number you want), Matthew can wash 100 cars in 14 hours or 7.14 cars an hour. Arianna can wash 100 cars in 11 hours or 9.09 cars an hour. Together, in an hour they can wash 7.14 + 9.09 or 16.23 cars. So to wash 100 cars it would take them 100/16.23 = 6.16 or about 6 hours. 
You can do this with variables as well. 
Matthew has a rate of x/14 while Arianna has a rate of x/11. Together their rate is x/14 + x/11= x/y
Divide both sides by x, you would get 1/14 + 1/11 = 1/y
Solve for y which would be around 6 hours. 

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

She sould do something that would push her confidents