how long to paint a room

Question

together, kris and her daughter kathy require 6 hr 24 min to paint a room. alone, kathy would require 24 hr more than kris. how long would it take kris to do the job alone? (convert minutes to hours)

Answer 1

Note that if you can finish the job in say 5 hours, that means that in hour, you get 1/5 of the job done.

 

let x be Kris’ time to complete the job, x+24 be Kathy’s time.

 

in one hour:

 

1/x + 1/(x+24) = 1/6.4

 

take LCD; do the algebra, and arrive at the following quadratic equation:

 

x² + 11.2x - 153.6.

 

can factor or use the quadratic formula. Discard the negative value since x should be positive.

 

x= 8 hours