Joe digs a ditch in 32 hours Joe working with George can did

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 ?

Solution

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