Last visit was: 21 May 2024, 13:15 It is currently 21 May 2024, 13:15
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Sam can complete a certain task in 4 hours while Peter needs only 3 ho

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625608 [11]
Given Kudos: 81918
Intern
Joined: 06 Jan 2018
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 0
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Own Kudos [?]: 1784 [0]
Given Kudos: 26
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6069
Own Kudos [?]: 4705 [2]
Given Kudos: 463
Location: India
GPA: 3.5
Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
2
Kudos
Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

Let the total work be 24 units

Efficiency of Sam is 6 units/hour
Efficiency of Peter is 8 units/hour

Work completed by Sam in half hour is 3 units, work left is 21 units

Combined efficiency of Sam and Peter is 14 units, so time required to complete the remaining piece of work is $$\frac{21}{14}$$ = $$\frac{3}{2}$$ Hours

Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35571 [1]
Given Kudos: 9464
Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
1
Kudos
Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

Less than a minute to solve: Break the problem into two stages. Use RT = W

Rates in jobs per hour:
Sam's rate (use in Stage 1): $$\frac{1}{4}$$
Peter's rate: $$\frac{1}{3}$$
Combined rate (use in Stage 2):
$$(\frac{1}{4}+ \frac{1}{3})=\frac{7}{12}$$

Convert Sam's time working alone:
30 minutes = $$\frac{1}{2}$$ hour*

Stage 1: Sam works alone

Total work is 1 (job)
How much work did Sam finish in 30 minutes?

R*T = W
R = $$\frac{1}{4}$$
T = $$\frac{1}{2}$$ hour
$$(\frac{1}{4}*\frac{1}{2})=\frac{1}{8}$$
of work is finished by Sam

How much work remains?
(Total W - Sam's W)
$$(1-\frac{1}{8})=\frac{7}{8}$$ of work remains for both to finish

Stage 2: they work together
How many hours will they need to finish the rest of the work?

R*T = W
R (combined, above): $$\frac{7}{12}$$
T = ?
W = $$\frac{7}{8}$$
$$\frac{7}{12}*T=\frac{7}{8}$$
$$T=(\frac{7}{8} * \frac{12}{7}) = \frac{12}{8}=\frac{3}{2}$$

*$$(30.mins*\frac{1hr}{60.mins})=\frac{30hr}{60}=\frac{1}{2}$$ hour
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18886
Own Kudos [?]: 22286 [0]
Given Kudos: 285
Location: United States (CA)
Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

We can let Sam’s rate = 1/4, and Peter’s rate = 1/3.

We can let the time Sam worked = 1/2 + x and the time Peter worked = x

Thus:

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

1/8 + x/4 + x/3 = 1

Multiplying the entire equation by 24, we have:

3 + 6x + 8x = 24

14x = 21

x = 21/14 = 3/2 hours

Intern
Joined: 29 Jul 2019
Posts: 18
Own Kudos [?]: 20 [1]
Given Kudos: 7
Location: United States (NJ)
GMAT 1: 750 Q49 V44
GPA: 3.51
Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
1
Kudos
I'm a bit thrown off by the wording of the question, particularly "to complete the task together?" Notably, it doesn't say "complete the remainder of the task together" nor does it say "complete the task working together" (which would also be ambiguous as you could read it as the time as though Sam did not already spend 30 min on it), so I'm reading this as the total time, including the 30 minutes Sam spends alone.

Bunuel, thoughts?
Intern
Joined: 12 Feb 2018
Posts: 13
Own Kudos [?]: 12 [0]
Given Kudos: 199
Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
Rate of Sam =1/4
Rate of peter=1/3
in 30 minutes, sam would have completed 1/8 of the work-->1/2*1/4=1/8
remaining 7/8 work has to be completed together
combined rate=7/12-->7/12 * X=7/8
ans=3/2 --option (A)
Intern
Joined: 11 May 2019
Posts: 2
Own Kudos [?]: 5 [0]
Given Kudos: 4
Location: United States
GMAT 1: 740 Q49 V41
GMAT 2: 770 Q50 V46
GPA: 2.7
Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
bcl wrote:
I'm a bit thrown off by the wording of the question, particularly "to complete the task together?" Notably, it doesn't say "complete the remainder of the task together" nor does it say "complete the task working together" (which would also be ambiguous as you could read it as the time as though Sam did not already spend 30 min on it), so I'm reading this as the total time, including the 30 minutes Sam spends alone.

Bunuel, thoughts?

I made the same "mistake." At least don't make another answer 2, which is what I selected because the entire job took two hours.
Non-Human User
Joined: 09 Sep 2013
Posts: 33140
Own Kudos [?]: 829 [0]
Given Kudos: 0
Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]
Moderator:
Math Expert
93373 posts