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bazaltina [42]
3 years ago
9

Jeff and Kirk can build 75 feet retaining wall together in 10 hours. Because Jeff has more experience, he could build the wall b

y himself 1 hour quicker than Kirk. How long would it take Kirk to build the wall by himself.
Mathematics
1 answer:
frez [133]3 years ago
7 0
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.
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