Jeff and Kirk can build a 75ft retaining wall together in 9

Jeff and Kirk can build a 75-ft retaining wall together in 9 hours. Because Jeff has more experience, he could build the wall by himself 2

hours quicker than Kirk. How long would it take Kirk (to the nearest minute) to build the wall by himself?

Solution

Let x=time it takes jeff by himself

then x+2 = time it takes kirk himself

This means Jeff, does 1/x th of a wall per hour, and Kirk does 1/(x+2) th of a wall per hour (each by himself)

Together they do 1/9 th of a wall per hour

So, the 2 hourly rates must add up to 1/9

1/x + 1/(x+2) = 1/9

So

x+2 + x = x(x+2)/9

18x + 18 = x^2 +2x

0= x^2 -16x - 18

Solve using quadratic equation:
x= [ 16 +/- sqrt (328)]/2

Throw away the negative answer to get:
x= 17.055 (time it takes Jeff alone )

So it would take Kirk one hour more or 19.055 hours (answer)