Last visit was: 19 Nov 2025, 21:05 It is currently 19 Nov 2025, 21:05
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,390
 [11]
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: 105,390
Kudos: 778,390
 [11]
Every morning Jim walks to his office at a certain constant speed whic 18 Jan 2022, 03:45
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

30% (02:47) correct 70% (03:29) wrong based on 50 sessions

History

Date
Time
Result
Not Attempted Yet
Every morning Jim walks to his office at a certain constant speed which enables him to arrive exactly on time. One fine morning he started walking at two-thirds his usual speed but after some time he realized that he was already 10 minutes behind at that point so he doubled his speed and reached his office 5 minutes early. What fraction of the total distance had Jim covered when he doubled his speed?

(A) 5/12
(B) 3/8
(C) 1/3
(D) 1/4
(E) 7/24



Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,707
 [2]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,707
 [2]
Every morning Jim walks to his office at a certain constant speed whic 23 Jan 2022, 10:28
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
Every morning Jim walks to his office at a certain constant speed which enables him to arrive exactly on time. One fine morning he started walking at two-thirds his usual speed but after some time he realized that he was already 10 minutes behind at that point so he doubled his speed and reached his office 5 minutes early. What fraction of the total distance had Jim covered when he doubled his speed?

(A) 5/12
(B) 3/8
(C) 1/3
(D) 1/4
(E) 7/24

Show more

You can do it through algebraic way too, but a logical way that can get you to the answer fast is
(I) If the ratio of speed for same distance is 1:2/3, the time taken would be 2/3:1.
Difference = \(x-\frac{2x}{3} = \frac{x}{3} = 10....x=30\) minutes
Time taken if covered in original speed = \(30*\frac{2}{3}=20\) minutes
(II) If the ratio of speed for distance in second part is 1:2*2/3, the time taken would be 2*2/3:1.
Difference = \(\frac{4x}{3}-x= \frac{x}{3} = 10+5....x=45\) minutes { 15 comes from covering 10 minutes and overall 5 less minutes}
Time taken if covered in original speed = \(45*\frac{4}{3}=60\) minutes

Total time is 80 minutes through original speed, out of which 20 minutes route is done at 2/3rd of original speed => \(\frac{20}{80} = \frac{1}{4}\)


D
avatar
jasminelin
avatar
Joined: 29 Jan 2022
Last visit: 13 Apr 2022
Posts: 11
Own Kudos:
4
Given Kudos: 7
Posts: 11
Kudos: 4
Every morning Jim walks to his office at a certain constant speed whic 23 Mar 2022, 20:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
Bunuel
Every morning Jim walks to his office at a certain constant speed which enables him to arrive exactly on time. One fine morning he started walking at two-thirds his usual speed but after some time he realized that he was already 10 minutes behind at that point so he doubled his speed and reached his office 5 minutes early. What fraction of the total distance had Jim covered when he doubled his speed?

(A) 5/12
(B) 3/8
(C) 1/3
(D) 1/4
(E) 7/24


You can do it through algebraic way too, but a logical way that can get you to the answer fast is
(I) If the ratio of speed for same distance is 1:2/3, the time taken would be 2/3:1.
Difference = \(x-\frac{2x}{3} = \frac{x}{3} = 10....x=30\) minutes
Time taken if covered in original speed = \(30*\frac{2}{3}=20\) minutes
(II) If the ratio of speed for distance in second part is 1:2*2/3, the time taken would be 2*2/3:1.
Difference = \(\frac{4x}{3}-1 = \frac{x}{3} = 10+5....x=45\) minutes { 15 comes from covering 10 minutes and overall 5 less minutes}
Time taken if covered in original speed = \(45*\frac{4}{3}=60\) minutes

Total time is 80 minutes through original speed, out of which 20 minutes route is done at 2/3rd of original speed => \(\frac{20}{80} = \frac{1}{4}\)


D
Show more

assume the original speed is 60mph for 60 min meaning the total distance is 60 miles
if the answer is D
2/3 speed is 40mph for (45/2) min which is 15 miles (which is where we get the 15/60=1/4 of the distance)
4/3 speed is 80mph for (135/4) min which is the remaining 45 miles
but then the total time spent is greater than 55 min (even though question says he arrives 5 min earlier)

????
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,707
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,707
Every morning Jim walks to his office at a certain constant speed whic 24 Mar 2022, 22:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jasminelin
chetan2u
Bunuel
Every morning Jim walks to his office at a certain constant speed which enables him to arrive exactly on time. One fine morning he started walking at two-thirds his usual speed but after some time he realized that he was already 10 minutes behind at that point so he doubled his speed and reached his office 5 minutes early. What fraction of the total distance had Jim covered when he doubled his speed?

(A) 5/12
(B) 3/8
(C) 1/3
(D) 1/4
(E) 7/24


You can do it through algebraic way too, but a logical way that can get you to the answer fast is
(I) If the ratio of speed for same distance is 1:2/3, the time taken would be 2/3:1.
Difference = \(x-\frac{2x}{3} = \frac{x}{3} = 10....x=30\) minutes
Time taken if covered in original speed = \(30*\frac{2}{3}=20\) minutes
(II) If the ratio of speed for distance in second part is 1:2*2/3, the time taken would be 2*2/3:1.
Difference = \(\frac{4x}{3}-1 = \frac{x}{3} = 10+5....x=45\) minutes { 15 comes from covering 10 minutes and overall 5 less minutes}
Time taken if covered in original speed = \(45*\frac{4}{3}=60\) minutes

Total time is 80 minutes through original speed, out of which 20 minutes route is done at 2/3rd of original speed => \(\frac{20}{80} = \frac{1}{4}\)


D

assume the original speed is 60mph for 60 min meaning the total distance is 60 miles
if the answer is D
2/3 speed is 40mph for (45/2) min which is 15 miles (which is where we get the 15/60=1/4 of the distance)
4/3 speed is 80mph for (135/4) min which is the remaining 45 miles
but then the total time spent is greater than 55 min (even though question says he arrives 5 min earlier)

????
Show more

That is not correct. You cannot assume all values as some would be interconnected.

If you want to test whether the solution for D in the earlier post is correct, you will have to take time as 80 minutes as that is the total time as per the solution.
Quote:

assume the original speed is 60mph for 80 min meaning the total distance is 80 miles
if the answer is D
2/3 speed is 40mph for 20 miles (which is where we get the 15/60=1/4 of the distance) => T = 20/40*60or 30 minutes
4/3 speed is 80mph for 60 miles => T = 60/80*60 or 3*15 or 45 minutes
but then the total time spent is greater than 55 min (even though question says he arrives 5 min earlier)
Total time 30+45 or 75, which is FIVE less than 80.
Show more

Hope it helps
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,707
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,707
 [1]
Every morning Jim walks to his office at a certain constant speed whic 24 Mar 2022, 22:30
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
Every morning Jim walks to his office at a certain constant speed which enables him to arrive exactly on time. One fine morning he started walking at two-thirds his usual speed but after some time he realized that he was already 10 minutes behind at that point so he doubled his speed and reached his office 5 minutes early. What fraction of the total distance had Jim covered when he doubled his speed?

(A) 5/12
(B) 3/8
(C) 1/3
(D) 1/4
(E) 7/24
Show more

ALGEBRAIC way

Let the distance traveled be d at a constant speed of x mph, and a out of total d be traveled at 2x/3 mph.

DISTANCE: a
Time taken on a normal day = \(\frac{a}{x}\)
Time taken on the specific day = \(\frac{a}{\frac{2x}{3}}=\frac{3a}{2x}\)
Thus, \(\frac{3a}{2x}-\frac{a}{x}=\frac{10}{60}.........\frac{a}{x}=\frac{1}{3}\)

DISTANCE: d-a
Time taken on a normal day = \(\frac{d-a}{x}\)
Time taken on the specific day = \(\frac{d-a}{\frac{4x}{3}}=\frac{3a}{4x}\)
Time saved is 5 minutes, so the time taken at increased speed would have saved 10+5 or 15 minutes.
Thus, \(\frac{d-a}{x}-\frac{3(d-a)}{4x}=\frac{(d-a)}{4x}=\frac{15}{60}.........\frac{d}{x}-\frac{a}{x}=1\)
\(\frac{d}{x}-\frac{1}{3}=1.........\frac{d}{x}=\frac{4}{3}\)


We are looking for the value of \(\frac{a}{d}\)
Now, \(\frac{\frac{a}{x}}{\frac{d}{x}}=\frac{a}{d}=\frac{\frac{1}{3}}{\frac{4}{3}}=\frac{1}{4}\)


D
User avatar
shivaniilall
User avatar
Joined: 22 Nov 2021
Last visit: 16 Oct 2025
Posts: 27
Own Kudos:
11
Given Kudos: 321
Location: India
Posts: 27
Kudos: 11
Every morning Jim walks to his office at a certain constant speed whic 31 Mar 2022, 05:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
Bunuel
Every morning Jim walks to his office at a certain constant speed which enables him to arrive exactly on time. One fine morning he started walking at two-thirds his usual speed but after some time he realized that he was already 10 minutes behind at that point so he doubled his speed and reached his office 5 minutes early. What fraction of the total distance had Jim covered when he doubled his speed?

(A) 5/12
(B) 3/8
(C) 1/3
(D) 1/4
(E) 7/24

ALGEBRAIC way

Let the distance traveled be d at a constant speed of x mph, and a out of total d be traveled at 2x/3 mph.

DISTANCE: a
Time taken on a normal day = \(\frac{a}{x}\)
Time taken on the specific day = \(\frac{a}{\frac{2x}{3}}=\frac{3a}{2x}\)
Thus, \(\frac{3a}{2x}-\frac{a}{x}=\frac{10}{60}.........\frac{a}{x}=\frac{1}{3}\)

DISTANCE: d-a
Time taken on a normal day = \(\frac{d-a}{x}\)
Time taken on the specific day = \(\frac{d-a}{\frac{4x}{3}}=\frac{3a}{4x}\)
Time saved is 5 minutes, so the time taken at increased speed would have saved 10+5 or 15 minutes.
Thus, \(\frac{d-a}{x}-\frac{3(d-a)}{4x}=\frac{(d-a)}{4x}=\frac{15}{60}.........\frac{d}{x}-\frac{a}{x}=1\)
\(\frac{d}{x}-\frac{1}{3}=1.........\frac{d}{x}=\frac{4}{3}\)


We are looking for the value of \(\frac{a}{d}\)
Now, \(\frac{\frac{a}{x}}{\frac{d}{x}}=\frac{a}{d}=\frac{\frac{1}{3}}{\frac{4}{3}}=\frac{1}{4}\)


D
Show more

Hello Sir,
Can you please explain this step to me?
User avatar
shivaniilall
User avatar
Joined: 22 Nov 2021
Last visit: 16 Oct 2025
Posts: 27
Own Kudos:
11
Given Kudos: 321
Location: India
Posts: 27
Kudos: 11
Every morning Jim walks to his office at a certain constant speed whic 31 Mar 2022, 05:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel, please provide with a solution. Thanks.
User avatar
Regor60
User avatar
Joined: 21 Nov 2021
Last visit: 17 Nov 2025
Posts: 528
Own Kudos:
383
 [2]
Given Kudos: 459
Posts: 528
Kudos: 383
 [2]
Every morning Jim walks to his office at a certain constant speed whic 31 Mar 2022, 06:27
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Set D to total distance, D1 to intermediate distance and R to original speed.

The first part of the problem translates to

D1/(2R/3) = D1/R + 10

The second part translates to

D1/(2R/3) + (D-D1)/(4R/3) =
D/R - 5

Clearing R from the denominator of the first and solving for R yields

R = D1/20

Clearing R from the denominator of the second yields

3D1/2 +3(D-D1)/4 = D-5R

Substituting for R=D1/20 and expanding the above yields

3D1/2 - 3D1/4 + 3D/4 = D -
D1/4

Multiplying through by 4

6D1 - 3D1 + 3D = 4D - D1

So

4D1 = D and D1/D = 1/4

Posted from my mobile device
User avatar
shivaniilall
User avatar
Joined: 22 Nov 2021
Last visit: 16 Oct 2025
Posts: 27
Own Kudos:
11
Given Kudos: 321
Location: India
Posts: 27
Kudos: 11
Every morning Jim walks to his office at a certain constant speed whic 02 Apr 2022, 00:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Regor60
Set D to total distance, D1 to intermediate distance and R to original speed.

The first part of the problem translates to

D1/(2R/3) = D1/R + 10

The second part translates to

D1/(2R/3) + (D-D1)/(4R/3) =
D/R - 5

Clearing R from the denominator of the first and solving for R yields

R = D1/20

Clearing R from the denominator of the second yields

3D1/2 +3(D-D1)/4 = D-5R

Substituting for R=D1/20 and expanding the above yields

3D1/2 - 3D1/4 + 3D/4 = D -
D1/4

Multiplying through by 4

6D1 - 3D1 + 3D = 4D - D1

So

4D1 = D and D1/D = 1/4

Posted from my mobile device
Show more


I could finally solve this question, all because of your solution :cry: Thank you so so so much!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
Every morning Jim walks to his office at a certain constant speed whic 21 Jul 2024, 00:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts