SOLUTION: Joe digs a ditch in 3.2 hours. Joe working with George can did the same length ditch in 2.7 hours. How long would it take George to dig the ditch by himself.

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Question 19150: Joe digs a ditch in 3.2 hours.
Joe working with George can did the same length ditch in 2.7 hours.
How long would it take George to dig the ditch by himself.
Answer by venugopalramana(3286) About Me  (Show Source):
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Joe digs a ditch in 3.2 hours.
Joe working with George can did the same length ditch in 2.7 hours.
How long would it take George to dig the ditch by himself.

Joe digs a ditch in 3.2 hours...so in 1 hour he digs 1/3.2 ditch=10/32=5/16
let george alone take x hrs to dig the ditch...so in 1 hour he digs 1/x ditch
so in 1 hour joe and george together dig 5/16+1/x ditch =(5x+16)/16x
so they take 16x/(5x+16) hrs to dig the ditch together
but this given as 2.7 hours
so 16x/(5x+16)=2.7
cross multiplying we get
16x=2.7(5x+16)=13.5x+43.2
16x-13.5x=43.2
2.5x=43.2
x=43.2/2.5=432/25=17.28 hours
so george alone takes 17.28 hrs to dig the ditch