how long does it take giselle to paint a barn by herself?

Question

katy can paint a barn in 6 hours by herself giselle and katy working together can paint a barn in 2.4 hours? how long does it take giselle to paint a barn by herself?

Answer 1

Katy can paint a barn in 6 hours  ==>

in one hour Katy can paint 1/6 of the barn

 

Katy and Giselle together can paint a barn in 2.4 hours  ==>  

in one hour Katy and Giselle can paint 1/2.4 of the barn  

 

Let X = how much of the barn Giselle can paint in one hour  

 

In one hour, the amount of the barn that Katy and Giselle can paint together (which is 1/2.4) must equal the sum of the amounts that they can paint individually (which are 1/6 and X).  So  

 

1/2.4 = 1/6 + X

 

Multiply both sides by (2.4)*6 to clear fractions and get

 

6 = 2.4 + 14.4X

14.4X = 3.6

X = 3.6/14.4 = 36/144 = 1/4  

 

So Giselle can paint 1/4 of the barn in one hour, therefore 

 

it will take Giselle 4 hours to paint a barn by herself