BTGModeratorVI wrote: ↑

Mon Sep 14, 2020 8:44 am

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

Answer: D
Source: Official guide

Let's assign a nice value to the TOTAL number of units produced on Friday.
We want a number that works well with the given numbers in the question (1/4 and 6)
So let's say a TOTAL of 24 units were produced

Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday.
1/4 of 24 = 6
In other words, machine K took 3 hours to produce 6 units
Rate = output/time = 6/3 = 2
So, machine K produces 2 units PER HOUR

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.
24 - 6 = 18
So, when machine M starts helping, the two machines have 18 units to produce
Rate = output/time = 18/6 = 3
So, the COMBINED rate of the two machines is 3 units PER HOUR

We already know that machine K produces 2 units PER HOUR
3 - 2 = 1, so machine M produces 1 unit PER HOUR


How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
Time = output/rate = 24/1 = 24

Answer: D

Cheers,
Brent