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talaangoshtari: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed May 21, 2014 4:29 am; Thanked: 8 times; Followed by:1 members

Work problem

by talaangoshtari » Thu May 07, 2015 4:26 am

Working alone at their respective constant rates, Audry can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audry and Ferris worked togegher on the job and completed it in 2 hours, but while Audry worked this entire time,Ferris worked for some of the time and took 3 breaks of eual length. How many minutes long was each of Ferris breaks?

A.5
B.10
C.15
D.20
E.25

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Source: Beat The GMAT — Problem Solving | Thu May 07, 2015 4:26 am

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by GMATGuruNY » Thu May 07, 2015 5:51 am

talaangoshtari wrote:Working alone at their respective constant rates, Audry can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audry and Ferris worked togegher on the job and completed it in 2 hours, but while Audry worked this entire time,Ferris worked for some of the time and took 3 breaks of eual length. How many minutes long was each of Ferris breaks?

A.5
B.10
C.15
D.20
E.25

Let the job = 12 widgets.

Since Audry can complete the job in 4 hours, Audry's rate = w/t = 12/4 = 3 widgets per hour.
Since Ferris can complete the job in 3 hours, Ferris's rate = 12/3 = 4 widgets per hour.

Since Audry works for the entire 2 hours at rate of 3 widgets per hour, the total work produced by Audry = r*t = 2*3 = 6 widgets.
Thus, the total work produced by Ferris = (total job) - (Audry's work) = 12-6 = 6 widgets.
Since Ferris produces 4 widgets per hour, the time for Ferris to produce the remaining 6 widgets = w/r = 6/4 = 1.5 hours.
Thus, the total time for Ferris's 3 breaks = 2 - 1.5 = 1/2 hour = 30 minutes, implying that each of the 3 breaks = 10 minutes.

The correct answer is B.

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Thu May 07, 2015 6:30 am

Working alone at their respective constant rates, Audry can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audry and Ferris worked togegher on the job and completed it in 2 hours, but while Audry worked this entire time,Ferris worked for some of the time and took 3 breaks of eual length. How many minutes long was each of Ferris breaks?

If Audry can do 1 job in 4 hours, her rate is 1/4. If she works for two hours she'll do (1/4) * 2 = 1/2 of the job.

So we know Ferris does the other 1/2 of the job.

If Ferris can do 1 job in 3 hours, his rate is 1/3. If he works for t hours, and does 1/2 a job, we know that (1/3) * t = 1/2. Solving for t, we get 3/2 = 1.5. If he worked for 1.5 of the 2 hours, he took a 1/2 hour, or 30 minute break. If he took 3 breaks, each break was 30/3 = 10 minutes long.

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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 am; Thanked: 29 times; Followed by:2 members

by gmatclubmember » Sun May 10, 2015 7:29 am

Aude efficiency is 25% work completion in 1 hr; and for Ferri this is 33% work completion in 1 hr.
In 2 hour ideally they would have completed - 25*2 +33*2 = 116% of work ; but instead they completed only 100% of work. So they are 16% behind schedule which is due to the breaks taken by Ferris. So ferris worked only 50% instead of 66 %. So Ferris didnt worked for 16% time. Since Ferris completes 33% work in 1 hr that would mean 16% would be 30 mins. So Ferris didnt worked for 30 mins. 3 equal breaks mean - each break lasted for 10 mins.

Note tht I have rounded 33.33 to 33 and 16.67 to 16.

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by Brent@GMATPrepNow » Mon Oct 21, 2019 8:11 am

talaangoshtari wrote:Working alone at their respective constant rates, Audry can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audry and Ferris worked togegher on the job and completed it in 2 hours, but while Audry worked this entire time,Ferris worked for some of the time and took 3 breaks of eual length. How many minutes long was each of Ferris breaks?

A.5
B.10
C.15
D.20
E.25

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Oct 23, 2019 5:58 pm

talaangoshtari wrote:Working alone at their respective constant rates, Audry can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audry and Ferris worked togegher on the job and completed it in 2 hours, but while Audry worked this entire time,Ferris worked for some of the time and took 3 breaks of eual length. How many minutes long was each of Ferris breaks?

A.5
B.10
C.15
D.20
E.25

We see that Audry's rate is 1/4 and Ferris' rate is 1/3. If Ferris didn't take any breaks, in 2 hours, they could complete 2(1/4) + 2(1/3) = 1/2 + 2/3 = 7/6 of the job. However, they really completed 1 job in 2 hours because Ferris took 3 breaks. The amount of work where Ferris took the breaks is equal to 7/6 - 1 = 1/6 of the job. SInce it would take Ferris (1/6)/(1/3) = 1/2 hour to complete 1/6 of the job, he must spend 1/2 hour = 30 minutes on his 3 breaks. Since each of his breaks is of equal length, he spent 30/3 = 10 minutes on each of his breaks.

Alternate Solution:

Since Audry completes the job in 4 hours all by herself, in two hours, she can complete 1/2 of the job, leaving Ferris to complete the remaining half.

If Ferris took no brakes, it would take him 1.5 hours = 90 minutes to complete half of the job since he can complete the whole job in 3 hours. Since it took him 2 hours = 120 minutes instead, he took a total of 120 - 90 = 30 minutes of break. Since each of his breaks is of equal length, he spent 30/3 = 10 minutes on each of his breaks.

Answer: B

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