SOLUTION: solve. approximate irrational roots to the nearest tenth. Together Anna and Carla can spray- paint a van in 8 hours. Alone it takes Anna 2 hours less than Carla. Find the time

Algebra ->  Real-numbers -> SOLUTION: solve. approximate irrational roots to the nearest tenth. Together Anna and Carla can spray- paint a van in 8 hours. Alone it takes Anna 2 hours less than Carla. Find the time       Log On


   

Question 44160: solve. approximate irrational roots to the nearest tenth.
Together Anna and Carla can spray- paint a van in 8 hours. Alone it takes Anna 2 hours less than Carla. Find the time it takes each of them to paint the van alone. Give your answers to the nearest tenth of an hour. (units optional)
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Let Carla's individual time be c. So Anna's time is c-2.
We set this one up like this
t/A + t/B = 1
8/c + 8/(c-2) = 1
now multiply by the LCD, c(c-2), and get
8(c-2) + 8c = c(c-2)
8c - 16 + 8c = c^2 - 2c
now collect like terms and solve...
c^2 - 18c + 16 = 0
This cannot be factored so let's try completing the square...
c^2 - 18c + 81 + 16 = 81
c^2 - 18c + 81 = 65
(c - 9)^2 = 65
c - 9 = ± √65
c = 9 ± √65
The negative root does not work since that would make Anna's time negative so Carla's time is
c = 9 + √65 or about 17.1 hours
Anna can do it in c-2 or about 15.1 hours