# How long did it take them to dig a hole?

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Three workmen set out to dig a hole.
On his own, Vikram can dig a hole in 18 minutes, Harish can dig a hole in 6 minutes and Mahesh can dig a hole in 5 minutes.
They started to dig this hole together.
Unfortunately, Mahesh had forgotten what he was supposed to be doing and was actually shovelling the dirt back into the hole at the same rate as he could have removed dirt.
Vikram and Harish never noticed this so how long did it take them to dig a hole?

posted Aug 6, 2018

45 minutes

Vikram- can do the job in 18 minutes ==> he can do 1/18 of the job in 1 min,
Harish- can do the job in 6 minutes ==> he can do 1/6 of the job in 1 min,
Mahesh- can do the job in 5 minutes ==> he can do 1/5 of the job in 1 min,
They started and spent x minutes to do the job that is equal to 1:
x*(1/18+1/6-1/5)=1 ==> x*2/90=1 ==> x=45 minutes

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