It take Kori 20 hours longer to paint a townhouse than it takes Chris. Working together they can do the job in 24 hours.

Question

It takes Kori 20 hours longer to paint a townhouse than it takes chris. Working together they can do the job in 24 hours. How long would it take each, working alone, to paint a townhouse?

Answer 1

Chris takes C hours to paint the townhouse

Kori takes C+20 hours to paint the townhouse

Their workrates are 1/C and 1/(C+20), respectively

The combined workrate is (1/C) + 1/(C+20) = [(C+20) + C]/ [C(C+20)]

= [ 2c + 20]/[C^2 + 20c]

Their time is [C^2 + 20c]/[2c+20] = 24

C^2 + 20c = 24(2c + 20)

C^2 + 20c = 48c + 480

C^2 - 28c - 480 = 0

( C - 40 )( C + 12 ) = 0

C = 40 or c = -12

It takes Chris 40 hours to paint the townhouse

It takes Kori 60 hours to paint the townhouse

1/40 + 1/60 = 100/2400 = 1/24

Working together, they will paint it in 24 hours