A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 18 minutes and a model N computer can complete the same task in 9 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?
Source: Gmat Hacks 1800
Time taken by model M computer to complete 1 work = 18 mins so Rate of work of model M = 1/18 work/min
Time taken by model N computer to complete 1 work = 9 mins so Rate of work of model N = 1/9 work/min
1 work was completed in 1 min so combined rate of work of x computers of M type and x computers of N type = 1 work/min
(because Work = Rate*Time)
x/18 + x/9 = 1 (Rates are additive)
x = 6
There are only two things to remember in work rate questions:
1. Rates are Additive.
2. Work = Rate*Time
(which implies Rate = 1/Time)
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