Last visit was: 19 Nov 2025, 06:51 It is currently 19 Nov 2025, 06:51
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
catinabox
User avatar
Joined: 27 Nov 2019
Last visit: 18 Nov 2025
Posts: 567
Own Kudos:
588
 [4]
Given Kudos: 223
Location: United States (IL)
Schools: Kellogg '24 (M)
GMAT 1: 770 Q50 V44
GPA: 4
Products:
GMAT Club Tests
Schools: Kellogg '24 (M)
GMAT 1: 770 Q50 V44
Posts: 567
Kudos: 588
 [4]
Olivia, Jacob, and Ethan are laying down tile flooring in a large Updated on: 14 Apr 2025, 06:08
Originally posted by catinabox on 11 Sep 2024, 14:16.
Last edited by Bunuel on 14 Apr 2025, 06:08, edited 1 time in total.
Edited the question.
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide Answer
Hide
Show
History
Shortest Time: 2 hours 13 minutes Longest Time: 2 hours 44 minutes
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

28% (02:22) correct 72% (02:48) wrong based on 563 sessions

History

Date
Time
Result
Not Attempted Yet
Olivia, Jacob, and Ethan are laying down tile flooring in a large hallway. Working alone at their respective rates, Olivia can tile the hallway in 6 hours, Jacob can tile the hallway in 4 hours, and Ethan can tile the hallway in 5 hours. To speed up the work, exactly two of them will work together to tile the hallway.

Select for Shortest Time the time closest to the least amount of time required for any 2-person team to complete the hallway, and select for Longest Time the time closest to the greatest amount of time required for any 2-person team to complete the hallway. Make only two selections, one in each column.
Shortest Time Longest Time
2 hours 2 minutes
2 hours 9 minutes
2 hours 13 minutes
2 hours 44 minutes
2 hours 54 minutes
3 hours 11 minutes
Submit Answer
Start the Timer above, select the radio buttons, and click "Submit" to add this question to your Error log.
ShowHide Answer
Official Answer
Shortest Time: 2 hours 13 minutes Longest Time: 2 hours 44 minutes
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,389
Own Kudos:
778,231
 [1]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,389
Kudos: 778,231
 [1]
Olivia, Jacob, and Ethan are laying down tile flooring in a large 14 Apr 2025, 06:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Official Solution:
Bunuel

Olivia, Jacob, and Ethan are laying down tile flooring in a large hallway. Working alone at their respective rates, Olivia can tile the hallway in 6 hours, Jacob can tile the hallway in 4 hours, and Ethan can tile the hallway in 5 hours. To speed up the work, exactly two of them will work together to tile the hallway.

Select for Shortest Time the time closest to the least amount of time required for any 2-person team to complete the hallway, and select for Longest Time the time closest to the greatest amount of time required for any 2-person team to complete the hallway. Make only two selections, one in each column.



Shortest TimeLongest Time
2 hours 2 minutes
2 hours 9 minutes
2 hours 13 minutes
2 hours 44 minutes
2 hours 54 minutes
Show more

Individual rates:

• Olivia — 1/6 hallway per hour

• Jacob — 1/4 hallway per hour

• Ethan — 1/5 hallway per hour

Fastest pair is Jacob and Ethan.

• Combined rate = 1/4 + 1/5 = 9/20 hallway per hour

• Time = 1/(9/20) = 20/9 hours

• 20/9 hours = 2 hours and 2/9 of an hour

• 2/9 * 60 minutes ≈ 13 minutes

So, time ≈ 2 hours 13 minutes

Slowest pair is Olivia and Ethan.

• Combined rate = 1/6 + 1/5 = 11/30 hallway per hour

• Time = 1/(11/30) = 30/11 hours

• 30/11 hours = 2 hours and 8/11 of an hour

• 8/11 * 60 minutes ≈ 44 minutes

So, time ≈ 2 hours 44 minutes


Correct answer:

Shortest Time "2 hours 13 minutes"

Longest Time "2 hours 44 minutes"
General Discussion
User avatar
siddhantvarma
User avatar
Joined: 12 May 2024
Last visit: 15 Nov 2025
Posts: 539
Own Kudos:
715
Given Kudos: 196
GMAT Focus 1: 635 Q87 V82 DI75
Products:
Forum Quiz
GMAT Focus 1: 635 Q87 V82 DI75
Posts: 539
Kudos: 715
Olivia, Jacob, and Ethan are laying down tile flooring in a large 12 Sep 2024, 10:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let w: work to tile the hallway
work = rate*time => w = rate*time
From this we can find the individual rate of all three:
Olivia's rate (\(r_o\)) = w/6
Jacob's rate (\(r_j\)) = w/4
Ethan's rate (\(r_e\)) = w/5

For shortest time, we need the largest values of rate and for the longest time, we need the smallest values of rate. This is because time is inversely proportional to rate.
We know: 1/4 > 1/5 > 1/6
This means \(r_j\) > \(r_e\) > \(r_o\)

For shortest time, we need the largest values of rate so we'll take Jacob and Ethan.
w = (\(r_j\) + \(r_e\))*time => w = (w/4 + w/5)*t => t = 20/9 hours
Converting to minutes we get 2 hours 13 minutes.

For longest time, we need the smallest values of rate so we'll take Olivia and Ethan.
w = (\(r_o\) + \(r_e\))*time => w = (w/6 + w/5)*t => t = 30/11 hours
Converting to minutes we get 2 hours 47 minutes.
User avatar
catinabox
User avatar
Joined: 27 Nov 2019
Last visit: 18 Nov 2025
Posts: 567
Own Kudos:
588
 [1]
Given Kudos: 223
Location: United States (IL)
Schools: Kellogg '24 (M)
GMAT 1: 770 Q50 V44
GPA: 4
Products:
GMAT Club Tests
Schools: Kellogg '24 (M)
GMAT 1: 770 Q50 V44
Posts: 567
Kudos: 588
 [1]
Olivia, Jacob, and Ethan are laying down tile flooring in a large 13 Sep 2024, 07:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
siddhantvarma
Let w: work to tile the hallway
work = rate*time => w = rate*time
From this we can find the individual rate of all three:
Olivia's rate (\(r_o\)) = w/6
Jacob's rate (\(r_j\)) = w/4
Ethan's rate (\(r_e\)) = w/5

For shortest time, we need the largest values of rate and for the longest time, we need the smallest values of rate. This is because time is inversely proportional to rate.
We know: 1/4 > 1/5 > 1/6
This means \(r_j\) > \(r_e\) > \(r_o\)

For shortest time, we need the largest values of rate so we'll take Jacob and Ethan.
w = (\(r_j\) + \(r_e\))*time => w = (w/4 + w/5)*t => t = 20/9 hours
Converting to minutes we get 2 hours 13 minutes.

For longest time, we need the smallest values of rate so we'll take Olivia and Ethan.
w = (\(r_o\) + \(r_e\))*time => w = (w/6 + w/5)*t => t = 30/11 hours
Converting to minutes we get 2 hours 47 minutes.
Show more

This is the correct solution.

Here is the official solution:

The first thing to note is:
Jacob and Ethan working together will always be the fastest. This is because Jacob has the highest individual rate (1 hallway per 4 hours), and Ethan’s rate (1 hallway per 5 hours) is the second-highest (or in the middle).

Olivia and Ethan will always be the slowest. This is because Olivia has the lowest rate (1 hallway per 6 hours), and with Ethan’s second-highest rate, the combined speed is still slower compared to other pairs.

This is a Work problem. These questions are always solved by looking at the rate of work which is expressed per unit of time such as 1/4th of hallway per hour can be done by Jacob.


1. Rate of Work
  • Olivia's rate: She can complete the hallway in 6 hours, so her rate is 1 hallway per 6 hours.
  • Jacob's rate: He can complete the hallway in 4 hours, so his rate is 1 hallway per 4 hours.
  • Ethan's rate: He can complete the hallway in 5 hours, so his rate is 1 hallway per 5 hours.

2. Combined Rates
When two people work together, their combined rate is the sum of their individual rates. The total time they take together to complete the hallway is calculated as:
Code:
Time = 1 / (combined rate)
A. Jacob and Ethan (Shortest Time)
  • Jacob's rate: 1 hallway per 4 hours
  • Ethan's rate: 1 hallway per 5 hours
The combined rate for Jacob and Ethan is:
Code:
Combined rate = (1/4) + (1/5) = 9/20 of a hallway per hour
Time taken for Jacob and Ethan together:
Code:
Time = 1 / (9/20) = 20/9 ≈ 2.22 hours (or about 2 hours 13 minutes)

B. Olivia and Ethan (Longest Time)
  • Olivia's rate: 1 hallway per 6 hours
  • Ethan's rate: 1 hallway per 5 hours
The combined rate for Olivia and Ethan is:
Code:
Combined rate = (1/6) + (1/5) = 11/30 of a hallway per hour
Time taken for Olivia and Ethan together:
Code:
Time = 1 / (11/30) = 30/11 ≈ 2.73 hours (or about 2 hours 44 minutes)
User avatar
HarshZsssh
User avatar
Joined: 20 Aug 2024
Last visit: 12 Apr 2025
Posts: 42
Own Kudos:
10
Given Kudos: 24
Posts: 42
Kudos: 10
Olivia, Jacob, and Ethan are laying down tile flooring in a large 12 Feb 2025, 06:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
assume total work done 120 hrs and than it is easy to find rate and combined rate
catinabox
Olivia, Jacob, and Ethan are laying down tile flooring in a large hallway. Working alone, Olivia can tile the hallway in 6 hours, Jacob can tile the hallway in 4 hours, and Ethan can tile the hallway in 5 hours. To speed up the work, two of them will work together to tile the hallway, with each person working at his or her respective rate.

Select the value closest to the shortest time in which a 2-person team could tile the hallway, and select the value closest to the longest time in which a 2-person team could tile the hallway. Make only two selections, one in each column.
Show more
Moderators:
Bunuel
Math Expert
105389 posts
kingbucky
496 posts