Question

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?

Answer 1

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
 Answer:
 Working together, it will take the two machines to produce 75 widgets about:
 t = 5 hours