SOLUTION: Working together, Camry, Kyoko, and Priscilla can dig a drainage ditch in 2.5 hours. Working alone, Priscilla can do it in 5 hours, while Camry can do it 3/4 hour faster than Kyoko

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Question 419083: Working together, Camry, Kyoko, and Priscilla can dig a drainage ditch in 2.5 hours. Working alone, Priscilla can do it in 5 hours, while Camry can do it 3/4 hour faster than Kyoko. Ho long will it take Kyoko to dig the ditch by herself? (Round the answer to 2 decimal places.)
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let k=number of hrs it takes Kyoko to do the job.
Priscilla can do 1/5 the job in 1 hr. Kyoko can do 1/k the job in 1 hr and Camry can do 1/(k-.75) the job in 1 hr. Together they can do 1/2.5 of the job in 1 hr.
1/5 + 1/k + 1/(k-.75)=1/2.5
.2 + 1/k + 1/(k-.75)=.4
.2k^2-.15k+k-.75+k=.4k^2-.3k Multiply each side by k^2-.75k
.2k^2-2.15k+.75=0
k=10.39 hrs Quadratic formula.
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Ed