Audrey 4 hours to complete a certain job. Ferris can do the

1. In 2 hours Audrey would have completed 1/2 of the job as he takes 4 hours to complete the job
2. Ferris completed the remaining half in those 2 hours
3. But Ferris would normally complete 1/2 of the job in 3/2 = 1.5 hours
4. So Ferris totally took break for 30 min and since he took 3 breaks of equal length , each break was 10 min long.

Portion Highlighted in red doesn't look to be correct..

1.7 hrs means 1 hr 42 minutes
total Time taken 120 minutes
So break size will be 6 minutes which is not even the answer...

0.3 Hr will be 18 minutes or 0.1 hr will be 6 minutes

Hi Bunuel,

Why can't we get answer by this method???

You would not get the answer by the above method because only Ferris took the break, So you need to get the breaks only from the time Ferris totally took. But above, you are instead calculating the time taken with both working and then trying to find the break time. But since Ferris took some breaks you would not get the answer this way.

Audrey works 4 hrs to get the job done. So in 2 hours Audrey completed 1/2 the work. To complete the remaining half Ferris needs only 1.5 hours that is 90 mins. However he took 3 breaks and finished the work in 2 hrs. Therefore Ferris took a break of 120 min - 90 mins = 30 mins spread across 3 equal sessions. So each break is 30/3 = 10 mins.

Option B.
Let the units of work be 12 units(LCM of 3,4)
A's rate=3u/hr
B's rate=4u/hr
A works continuously for 3 hrs,So A will complete 6u of work.
The remaining will be completed by F in 2 hrs.
Now F' rate without break is 8u in 2 hrs.But actually he did only 6u in 2 hrs.
So the time he take to complete 2u=Time he spent on breaks.
60 min=4u
So 15 min=1u
And 30 min=2 u
Divide by 3 we get 10.

Portion Highlighted in red doesn't look to be correct..

1.7 hrs means 1 hr 42 minutes
total Time taken 120 minutes
So break size will be 6 minutes which is not even the answer...

0.3 Hr will be 18 minutes or 0.1 hr will be 6 minutes

Hi Bunuel,

Why can't we get answer by this method???[/quote]

You would not get the answer by the above method because only Ferris took the break, So you need to get the breaks only from the time Ferris totally took. But above, you are instead calculating the time taken with both working and then trying to find the break time. But since Ferris took some breaks you would not get the answer this way


Adding to the above.......

Combined rate, if calculated, comes up = 7/12, so time taken = 12/7

However, given that both combined took time of 2 hours, so the given information supersedes the calculated part, hence this approach cannot be taken

........................ Rate ................. Time .................. Work


Audrey ............. \(\frac{1}{4}\) ..................... 4 ..................... 1

Ferris ............... \(\frac{1}{3}\) ..................... 3 ...................... 1

Combined .................................... 2 ........................... This is the given information inclusive of 3 breaks

Audrey worked nonstop for 2 hours, work done \(= \frac{1}{4} * 2 = \frac{1}{2}\)

Work left over for Ferris \(= 1 - \frac{1}{2} = \frac{1}{2}\)

Time required by Ferris\(= \frac{1}{2} * 3 = 1.5\)

Break taken by Ferris = 2 - 1.5 = 0.5 = 30 Minutes

Each break = 10 Minutes

Answer = B

WHAT IS THE PROBLEM IN BELOW METHOD:

y=total time of 3 breaks

1/4+1/(3+y)=1/2
y=1 hours and thus each break 20 mins long
What I am doing wrong?

I did this a completely different way that may not be optimal.

so A does a rate of 1/4 per hour and F does a rate of 1/3 per hour. Convert those to 4/12 (for F) and 3/12 (for A).

We know that A worked for the full 2 hours so A did 6/12 of the job, which means that F completed 6/12 of the job.

If F took no breaks, he would have completed 8/12, but we only need 6/12 so we have a difference of 2/12. So F need take breaks for a total of 1/4 of the total time.
1/4 of two hours is 30 mins and he took 3 breaks (30/3=10). Each break = 10 mins

B

Presenting the detailed solution

Given
We are told about the time taken by Audrey and Ferris to do a work(let's say W) i.e. 4 hours and 3 hours respectively. We are also told that both of them working together take 2 hours to complete the job. However during these 2 hours, Ferris took 3 breaks of equal time intervals whereas Audrey worked for the full 2 hours. We are asked to find the time taken by Ferris for each break.

Approach
We know that Work = Rate * Time. Since we are given the time taken by both Audrey & Ferris to do a particular work we can find out their respective rates in terms of work done i.e. W
For the situation when both of them are working together, we know the following:

a. Amount of work to be done i.e. W
b. Rate of work done by Audrey & Ferris in terms of W
c. Time for which Audrey worked

We can use the above information and the time rate equation to find out the time for which Ferris worked which can be used to calculate the time taken by Ferris for each break.

Working Out
Let the amount of work done be W.

Rate at which Audrey works
\(W = Ra * 4\) i.e. \(Ra = \frac{W}{4}\)

Rate at which Ferris works
Similarly \(Rb = \frac{W}{3}\)

Both Audrey & Ferris working together
Let's assume the time for which Ferris worked be t.

\(W = Ra * 2 + Rb * t\)

\(W = \frac{W}{4} * 2 + \frac{W}{3} * t\)

\(t = 1.5\) hours. Since Ferris worked for 1.5 hours, he took a total break of ( 2 - 1.5) hours = 30 minutes. Since he took 3 equal breaks his each break length = \(\frac{30}{3} = 10\) minutes.

Hope this helps

Regards
Harsh

Perfect logic.
I would just explain this "So F need take breaks for a total of 1/4 of the total time."
Since his rate of work is 4/12 and he does 6/12 of the work, time taken = Work/Rate = (6/12)/(4/12) = 1.5 hrs.
So he took a break for half an hour i.e. 30 mins and then proceed.

if ferris takes no breaks, then in 2 hours
he and audrey can complete 2(1/4+1/3), or 7/6 of the job
thus, ferris' total break time accounts for 1/6 of the job
if ferris can do entire job in 3 hours, then he can do 1/6 of job in 1/2 hour
1/2 hour=30 minutes
30/3=10 minutes per break
B

Let the total work be 12

Efficiency of Audrey = 3
Efficiency of Ferris = 4

Let total break of Ferris be x Hour

SO, 3*2 + 4 ( x - 2 ) = 12

Or, 6 + 4x - 8 = 12

Or, 4x = 24

Or, x = 6

Thus each of Ferris break was 6/60 hrs = 10 minutes...

Answer will be (B) 10 minutes...

The rate of Audrey is 1/4 and the rate of Ferris is 1/3.

If we let each break of Ferris equal x, his time worked is 2 - 3x ad Audrey’s time is 2. We can create the following equation and solve for x:

(1/4)(2) + (1/3)(2 - 3x) = 1

Multiplying by 12 we have:

6 + 4(2 - 3x) = 12

8 - 12x = 6

2 = 12x

1/6 = x

So each break was 1/6 x 60 = 10 minutes long.

Audrey can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours.
So, Audrey's RATE = 1/4 of the job per hour
And Ferris' RATE = 1/3 of the job per hour

Audrey and Ferris worked together on the job and completed it in 2 hours, but while Audrey worked this entire time, Ferris worked for some of the time and took 3 breaks of equal length.
Since Audrey works for the entire 2 hours, let's determine how much work she does.
At a rate of 1/4 of the job per hour, Audrey can complete 1/2 of the job in TWO hours.

This means Ferris must have completed the other 1/2 of the job

Time = output/rate
So, Ferris' work time = (1/2)/(1/3) = 3/2 hours = 90 MINUTES

So, at his normal rate of work, Ferris can complete his half of the job in 90 MINUTES, which meanshe rested for the other 30 minutes.


How many minutes long was each of Ferris's break?
Ferris took 3 breaks of equal length
If he rested for a TOTAL of 30 minutes, each break was 10 minutes long.

Answer: B

Cheers,
Brent

Audrey worked for 2 hours and Ferris worked X amount of hours less than Audrey.

2/4 + (2-x)/3 = 1

-> 8 - 4x + 6 = 12
-> x= 1/2

So in total ferris didn't work for half an hour.
30 minutes divided by 3 is 10 minutes. Each break was 10 minutes.