megafan wrote:

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?

(A) 2

(B) 3

(C) 6

(D) 9

(E) 12

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

Answer (C)

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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