Rate and work

[RiyaR]

Working alone at its constant rate, machine K took 3 hours to produce 1/4
of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday.How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?

A)8
B)12
C)16
D)24
E)30

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Hi RiyaR,

As wordy and complex as this question might first appear, you can break it down into pieces and solve with very little in the way of tough calculations.

We're told....

Machine K took 3 hours to produce 1/4 of the units. From this, we have a rate (every 3 hours another 1/4 of the units are produced).

Machines K and M took 6 more hours to finish producing the rest of the units. Let's break this into two pieces:

Machine K worked for 6 more hours
Machine M worked for 6 hours

We know Machine K's rate: 3 hours to complete 1/4 of the units. Since it worked 6 more hours, Machine K completed 2(1/4) = 1/2 of the units during that time. Counting the initial 3 hours (and 1/4 of the units) that Machine K worked, it completed 1/4 + 1/2 = 3/4 of the units.

The remaining 1/4 of the units must have been produced by Machine M over the course of those 6 hours....

Machine M takes 6 hours to produce 1/4 of the units.

We're asked how long it would take Machine M to produce ALL of the units...

6 hours to produce 1/4 of the units =
24 hours to produce all of the units.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Mathsbuddy]

Here are the raw facts:
K Rate = 0.25/3 = 2/24
K+M Rate = 0.75/6 = 3/24
M Rate = 1/T
Find T

K+M Rate = K Rate + M Rate
So M Rate = K+M Rate - K Rate
1/T = 3/24 - 2/24 = 1/24
So T = 24
ANSWER = (D)