Math using the quadratic equation

Question

A small pipe can fill a tank in 9 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 6 min. How long would it take each pipe, working alone, to fill the tank?

Answer 1

Together the pipes fill the tank in 6 minutes, which means they fill 1/6 of the tank each minute.

The large pipe fills the tank in x minutes, which means it fills 1/x of the tank each minute.

The small pipe fills the tank in x+9 minutes, which means it fills 1/(x+9) of the tack each minute.

 

1/x + 1/(x+9) = 1/6

 

Now eliminate the denominators by multiplying each term by the least common multiple, which is 6x² + 54x.

 

6x + 54 + 6x = x² + 9x

x² - 3x - 54 = 0

 

So a=1, b=-3, c=-54.  Plug that into the quadratic equation.  What do you get?