eff and Kirk can build a​ 75-ft retaining wall together in 44 hours. Because Jeff has more​ experience, he could build the wall by himself 22 hours quicker than Kirk.

Question

Jeff and Kirk can build a​ 75-ft retaining wall together in 44 hours. Because Jeff has more​ experience, he could build the wall by himself 22 hours quicker than Kirk. How long would it take Kirk​ (to the nearest​ minute) to build the wall by​ himself?

Answer 1

Their combined work-rate is 1/44 of the wall per hour.

Kirk's work rate is 1/x , as he can build the wall by himself in x hours

Jeff can build the wall in (x-22) hours, so his work rate is 1/(x-22)

1/x + 1/(x-22) = 1/44

Multiplies by 44x(x-22):

44(x-22) + 44x = x(x-22)

44(x-22) + 44x = x^2 - 22x

0 = x^2 - 22x - 44(x-22)

= x^2 - 22x - 44x + 968

= x^2 - 66x + 968

(x - 44)(x-22)

x = 44 or x=22

x=22 is disqualified because it results in division by zero

x=44 hours = 2640 minutes