SOLUTION: Big Ben can dig the entire ditch network in 6 days. John Stud can dig it in 4 days. Paul Bunyan can dig it in 3 days. How long would it take if they all work together? They

Question 1160085: Big Ben can dig the
entire ditch network in 6
days. John Stud can dig it in
4 days. Paul Bunyan can
dig it in 3 days. How long
would it take if they all work
together?
They would get the job done in ______ days.
Found 4 solutions by josgarithmetic, saw, greenestamps, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
, their combined rate.

Number of days is the reciprocal of that.
Answer by saw(34)   (Show Source): You can put this solution on YOUR website!
Big Ben digs 1/6 per day
John Stud digs 1/4 per day
Paul Bunyan digs 1/3 per day
1/6+1/4+1/3 = 3/4 per day
So it means they would get the job done in 4/3 = 1.33333, 1 day and 8 hours.
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

For anyone who likes to avoid working with fractions, here is an alternative method for solving this kind of problem.

The given times for the three workers are 6, 4, and 3 days.

Consider the least common multiple of those numbers, which is 12 days. In 12 days...

Big Ben could dig 12/6 = 2 ditches;
John Stud could dig 12/4 = 3 ditches; and
Paul Bunyan could dig 12/3 = 4 ditches.

So in 12 days the three together could dig 2+3+4 = 9 ditches; that means the number of days it would take the three of them together to dig ONE ditch is 12/9 = 4/3.

Answer by ikleyn(52878)   (Show Source): You can put this solution on YOUR website!
.

Note to the post by @saw.

When the problem says "per day", it does not necessary mean that workers work 24 hours "per day".

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