The westminster widget company has an old machine that can produce 10 widgets in two hours. now they have purchased a new machine that can produce 30 widgets in three hours. working together, how long will it take the two machines to produce 75 widgets?

First we will find the average production for each machine:
 For old machine:
 (10) / (2) = 5 widgets / hour
 For new machine:
 (30) / (3) = 10 widgets / hour
 We define t:
 t = Amount of time in hours:
 The equation sought is:
 5 + 10 = 75 / t
 Clearing we have:
 t = (75 / (5 + 10))
 t = 5 hours
 
 Working together, it will take the two machines to produce 75 widgets about:
 t = 5 hours

The answer is the numbers between =5 and 5