Nancy can mow a yard in 3 hours and Peter can mow it in 4 hours. Suppose they both work together, how long would it take to finish?
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Nancy mows 1/3 yards per hour, Peter mows 1/4 yards per hour.
Does that help?
Much depends on whether Peter and Nancy like each other. But leaving that aside, philips13 is pointing you in the right direction.
let the total work to be done be 'w'
so nancy does it 3hrs, and peter in 4hrs.
so in hour nancy does one third of the work that is (w/3). and peter similarly does (w/4) in one hour
now suppose they work together for 'x' hours to get the work done
so nancy will do x*(w/3) at the rate of w/3 per hour and peter will do x*(w/4) at the rate of w/4 per hour.
now. this total work by nancy and peter combined, in x hours would be equilvalent to 'w'.
as you see 'w' gets cancelled out
now you can solve 'x' from the equation, which is the no. of hours they need to work together for!!!
post the answer you get!!!