Question

Jeff and Kirk can build 75 feet retaining wall together in 10 hours. Because Jeff has more experience, he could build the wall by himself 1 hour quicker than Kirk. How long would it take Kirk to build the wall by himself.

Answer 1

Let J and K be the times of Jeff and Kirk respectively
To know the time it takes two people to perform a task together use the equation:
$\frac{1}{J}+ \frac{1}{K}= \frac{1}{10}$
We also know from the problem that J=K-1, so
$\frac{1}{K-1}+ \frac{1}{K}= \frac{1}{10}$
Now get common denominators
$\frac{K}{K(K-1)}+ \frac{K-1}{K(K-1)}= \frac{1}{10}$
$\frac{K+K-1}{K(K-1)}= \frac{1}{10}$
Take reciprocals
$\frac{K(K-1)}{2K-1}=10$
$K(K-1)=10(2K-1)$
$K^{2} -K=20K-10$
$K^{2} -21K+10=0$
By the quadratic equation:
K=20.512
J=K-1=19.512
Putting these into the original formula for two people working together on a task
$\frac{1}{20.512}+ \frac{1}{19.512}= \frac{1}{10}$
So it checks out.