Explanation

Let's focus on 1 machine at a time and list the starting and stopping time.
We'll start with Machine A

MONDAY
12 noon: Machine A starts

TUESDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

WEDNESDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

THURSDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

FRIDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

SATURDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

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Now let's add Machine B

MONDAY
12 noon: Machine A starts
12 noon: Machine B starts

TUESDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

WEDNESDAY
4:00 am: Machine B stops
8:00 am: Machine A stops
12:00 noon: Machine A starts
12:00 noon: Machine B starts

THURSDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

FRIDAY
4:00 am: Machine B stops
8:00 am: Machine A stops
12:00 noon: Machine A starts
12:00 noon: Machine B starts

SATURDAY
8:00 am: Machine A stops
12:00 noon: Machine A starts

As we can see, both machines are stopped at the same time on Wednesday and Friday.

Answer: C and E

Cheers,
Brent
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is there any quicker method to do this calculation?

both machines should stop at a 40 hours interval [ as the LCM of 20,40 is 40]
so, starting from 12.00 noon of Monday we can take a 40 hour working time followed by a rest .
thus, 12noo+40 hours lead to a rest on Wednesday
again another 40 hours, now it's on Friday.

Yes we can find the LCM of total hours in order to have answer
eg: LCM of 24 hrs and 48 hrs

Yes we can find the LCM of total hours in order to have answer
eg: LCM of 24 hrs and 48 hrs

i saw this question in the ETS practice book but was a bit confused by the wording...
thought that "following saturday" meant we needed to calculate two weeks worth, which would mean it would include Monday...
was wondering if that confused anyone else?

For Machine A: For 20 hours of work, it takes 4 hours rest
=> In a span of 24 hours, the last 4 hours are for rest ... (i)

For Machine B: For 40 hours of work, it takes 8 hours rest
=> In a span of 48 hours, the last 8 hours are for rest ... (ii)

Thus, for the last 4 hours (out of the 8 hours) when Machine B is at rest, Machine A is also at rest.
This scenario occurs at the end of the 2nd day from when both A and B have started to work together

Thus, in every 2 days (48 hours), both machines are at rest in the last 4 hours

The machines start on Monday 12 noon

# First time both rest are the last 4 hrs of the 2nd day i.e. 8 am to 12 noon of Wednesday
(after this, both start working together from 12 noon of Wednesday)

# Thus, the second time both rest are the last 4 hrs of the 2nd day from Wednesday i.e. 8 am to 12 noon of Friday

There would be no more opportunities of resting together since they work only till Saturday.

Answers: C and E
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With such exercises I feel they look harder then they are.

Starting off with looking at mac a

mac a works 20hr and then rests 4 hr

Meaning that we would see their cycle looking like the following 20 work 4 rest= 24 hr, 24+20work + 4rest= 48 hr

Now B goes 40 work + 8 rest =48hr , 48+40work+8rest= 96hr

Now a thing we can spot or search for is how long does it take the lower one to catch up with the bigger one logic.

We look at A--> A will start their second round of rest at 44hr, which coincides with the rest of B.

Meaning that at the beginning of every second rest from A the two will rest simultaneously.

This leading us to the conclusion that every 44 hours the two will rest together for 4 hr.

This would mean the first rest that the two will have together will be on WED-->12+24+8=44-->leaving us with 16 hr left in wed

the next rest will be on friday 16+24+4=44-->leaving us with 20+12 hr from friday and saturday which is not enough to get a rest in together

Thereby getting the answers c and e

Hi, can you explain me how you get the result by LCM?
Thx,Regards

Process
Since they start on Monday and work until Saturday, they have 5x24 = 120 hours of work. This never intuitively clicks in my brain so, if you're like me, here's proof:
- 24 hours between 12pm Mon and 12pm Tue -> 24 hrs. total so far
- 24 hours between 12pm Tue and 12pm Wed -> 48 hrs. total so far
- 24 hours between 12pm Wed and 12pm Thu -> 72 hrs. total so far
- 24 hours between 12pm Thu and 12pm Fri -> 96 hrs. total so far
- 24 hours between 12pm Fri and 12pm Sat -> 120 hrs. total

Let's define a "day" as being the time span between 12 noon and the next 12 noon (e.g. 12pm Mon to 12pm Tue):

Machine A rests during the last four hours of each day: 8am to 12pm.

Machine B rests during the last eight hours of each two-day cycle: 4am to 12pm.

That means that, whenever Machine B is resting, Machine A also has to be resting. Since we're interested in overlap, we only need to worry about Machine B.

Let's find multiples of 48 between 0 and 120: 48, 96.

What would those times correspond to?
- 12pm Wednesday --> C
- 12pm Friday --> E

Hence, C and E.