Working alone at their respective constant rates, Ajay can c

Question

Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while firoz can do the same job in 3 hours.ajay and firoz worked together on the job and completed it in 2 hour, but while Ajay worked this entire time, firoz worked for some of the time and took 3 breaks of equal length. How Many minutes long were each of firoz breaks?

A)5 minutes
B)10 minutes
C)15 minutes
D)20 minutes
E)25 minutes

Need explanation

Posted from my mobile device

A)5 minutes
B)10 minutes 
C)15 minutes 
D)20 minutes 
E)25 minutes

Need explanation

Posted from my mobile device

GMATGuruNY · Accepted Answer

Let the job = the LCM of the 3 times = 12 widgets.

Since Ajay takes 4 hours to complete the 12-widget job, Ajay's rate  = \frac{work}{time} = \frac{12}{4} = 3  widgets per hour.
Since Firoz takes 3 hours to complete the 12-widget job, Firoz's rate  = \frac{work}{time} = \frac{12}{3} = 4  widgets per hour.

Since Ajay works for the entire 2 hours at a rate 3 widgets per hour, Ajay's work = (rate)(time) = 3*2 = 6 widgets.
Since Firoz works at a rate of 4 widgets per hour, the time for Firoz to produce the remaining 6 widgets of the 12-widget job  = \frac{work}{rate} = \frac{6}{4} = 1.5  hours.
Since Firoz work for 1.5 hours of the 2-hour job, his time for breaks = 30 minutes.
Since there are 3 breaks of equal length, the time for each break  = \frac{30}{3} = 10  minutes.

B

CrackverbalGMAT · Answer

In time and Work, completion of work = 1

When 2 or more people work for different time periods, then the sum of the fractions of work done by each person = 1

Work done by Ajay in 1 hour =  \frac{1}{4}

Work done by Firoz in 1 hour =  \frac{1}{3}

Fraction of work done by Ajay in 2 hours =  \frac{2}{4}  =  \frac{1}{2}

Let length of Firoz's break = x hours each (This is what we need to find)

Total Length of the break = 3x hours

Amount of time worked by Firoz = 2 - 3x hours

Fraction of work done by Firoz in 2 hours =  \frac{2 - 3x}{3}

Therefore  \frac{1}{2} +  \frac{2 - 3x}{3} = 1

\frac{3 + 2 *(2 - 3x)}{6} = 1

3 + 4 - 6x = 6

6x = 1

x =  \frac{1}{6} hours =  \frac{1}{6} * 60  = 10 minutes

Option B

Arun Kumar

Mona2019 · Answer

Ajay and Firoz worked together for 2 hours.
As Ajay completes the job in 4 hours, in 2 hours, he should have completed half of the work/job.
The remaining half must have been done by Firoz.

Firoz takes 3 hours to complete the job,
so he takes 3/2 hours to complete half of the job.

But he has taken 2 hours with breaks for half of the job.
so the extra time taken is due to break.
hence the extra time can be calculated by :
 2 hours -\frac{3}{2} hours =0.5 hours = 30 minutes.

so his 3 equal length breaks account for 30 minutes.
so each break should last for 10 minutes.

Fdambro294 · Answer

We are told the 2 people complete the job in 2 hours.

Ajay works at a Rate = (1/4) job per hour

Over the course of 2 hours, the amount of the job that Ajay will have completed is =

(1/4) * 2 hours = 2/4 = 1/2 of Job

This means that over the 2 hours, Firaz must have completed the other 1/2 of Job.

(1st) Usual Time it would take Firaz to complete 1/2 of Job with NO BREAKS.

Firaz’s Rate = (1/3) job per hour

Let T = Time it would take Firaz to complete 1/2 of the Job if he took NO BREAKS

(1/3) * T = 1/2

T = 3/2 hours

However, Firaz ACTUALLY “works” for 2 hours to complete his portion of the work when they work together.

2 hours = 4/2 hours that Firaz spent ACTUALLY working and taking breaks

-

3/2 hours it SHOULD have taken Firaz had he worked with NO BREAKS

=

1/2 hour EXTRA Time in which Firaz did not work

This 30 minutes of time NOT spent working is broken up over 3 equal breaks

Therefore, each break is 10 minutes long

-B-

Posted from my mobile device

KarishmaB · Answer

Since Ajay completes the work in 4 hrs, in 2 hrs, he would have done half the work. So the other half of the work was done by Feroz.

Feroz takes 3 hrs to complete the work so his rate is 1/3 work every hour. How long will be he take to complete 1/2 the work?

Time = Work/Rate  = \frac{(1/2)}{(1/3)} = 3/2  hrs

He completes this work in 1.5 hrs so for the other 0.5 hrs i.e. 30 mins, Feroz takes a break. So his each break must have been of 10 mins.

Answer (B)

chhabraspaceman · Answer

If they took a total of 2 Hours to complete the work
by calculating the time taken by them to do work without break at their respective combined rate would be:
12/7 hours or 1.7 hours which is equal to 102 minutes.
By subtracting 102 from 120 ( Total Time taken by them to complete the work) , i got 18 mins
and if the break were of equal length then 18/3 = 6 
Answer should be 6 minutes.

This was my Logic.
Kindly explain the mistake

Working alone at their respective constant rates, Ajay can c

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Working alone at their respective constant rates, Ajay can c

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards