Last visit was: 08 Jul 2025, 11:32 It is currently 08 Jul 2025, 11:32
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
prince00113
Joined: 17 Mar 2015
Last visit: 23 Jun 2019
Posts: 70
Own Kudos:
266
 [19]
Given Kudos: 64
Products:
Posts: 70
Kudos: 266
 [19]
2
Kudos
Add Kudos
17
Bookmarks
Bookmark this Post
avatar
alnewton
Joined: 15 May 2012
Last visit: 22 Sep 2021
Posts: 15
Own Kudos:
10
 [4]
Given Kudos: 21
Posts: 15
Kudos: 10
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 08 Jul 2025
Posts: 11,296
Own Kudos:
41,612
 [3]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,296
Kudos: 41,612
 [3]
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
User avatar
techiesam
Joined: 01 Jun 2015
Last visit: 14 Dec 2019
Posts: 157
Own Kudos:
327
 [1]
Given Kudos: 197
Location: India
Concentration: Strategy, International Business
GMAT 1: 620 Q48 V26
GMAT 1: 620 Q48 V26
Posts: 157
Kudos: 327
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
chetan2u
prince00113
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24


Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B

chetan2u

I have applied the same reasoning but I concluded that Amit traveled (x+y) m.And my final answer was 5/12.

<-----Amit----><------Rahul------>
---------------------------------------
<-------y------>/<-----------x------->

Can you please explain why Amit traveled 2x+y ??
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 08 Jul 2025
Posts: 11,296
Own Kudos:
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,296
Kudos: 41,612
Kudos
Add Kudos
Bookmarks
Bookmark this Post
techiesam
chetan2u
prince00113
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24


Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B

chetan2u

I have applied the same reasoning but I concluded that Amit traveled (x+y) m.And my final answer was 5/12.


---------------------------------------
/

Can you please explain why Amit traveled 2x+y ??


Hi..
Rahul is x ahead of Amit, but then in 20 secs, goes ahead of Rahul by x..
So if Rahul travelled y...
Position at start..
A.....<--x--->.....R
In 20 secs..
|<--x-->|<--y-->|R|<--x-->A
So R traveled y, while A traveled x+y+x
User avatar
techiesam
Joined: 01 Jun 2015
Last visit: 14 Dec 2019
Posts: 157
Own Kudos:
Given Kudos: 197
Location: India
Concentration: Strategy, International Business
GMAT 1: 620 Q48 V26
GMAT 1: 620 Q48 V26
Posts: 157
Kudos: 327
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thank you.The wording was little confusing.Could this type of question appear on gmat?
avatar
BYZ
Joined: 30 Dec 2015
Last visit: 03 Jan 2023
Posts: 3
Own Kudos:
5
 [1]
Given Kudos: 3
Posts: 3
Kudos: 5
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
let A be the speed of Amit and R be the speed of Raul
the speed of R is 1/60 (fraction of race/sec)
there for the speed of A is 1/48
Amit took 10sec to catch up to Raul and 10 more seconds to beat him by x meters
therefore the total distance the Raul travelled would be: 10/48 = 5/24
User avatar
Fdambro294
Joined: 10 Jul 2019
Last visit: 06 Apr 2025
Posts: 1,353
Own Kudos:
Given Kudos: 1,658
Posts: 1,353
Kudos: 705
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u

I think I answered my own question. My brain is fried tonight for some reason. So I might as well double check.

In the question, Rahul is running those first X meters before Amit even starts.

“Head-start” in this sense means he started running for some time before Amit even left. It doesn’t mean that Rahul started at a line that was X meters ahead of where Amir started.

In other words, they both started running from the same starting line. Rahul just left earlier.

I don’t know why the word “head start” was causing my brain to close up.

chetan2u
prince00113
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24


Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B

Posted from my mobile device
User avatar
Fdambro294
Joined: 10 Jul 2019
Last visit: 06 Apr 2025
Posts: 1,353
Own Kudos:
Given Kudos: 1,658
Posts: 1,353
Kudos: 705
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I didn’t follow this approach, but I do know that the answer you got answers the question of how much A covered when he was X meters ahead of R......NOT when A passed R and they were even.

techiesam
chetan2u
prince00113
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?

a. 1/6

b. 5/24

c. 1/4

d. 7/24

e. 11/24


Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..

Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..

Fraction = 5x/24x=5/24

B

chetan2u

I have applied the same reasoning but I concluded that Amit traveled (x+y) m.And my final answer was 5/12.


---------------------------------------
/

Can you please explain why Amit traveled 2x+y ??

Posted from my mobile device
User avatar
Fdambro294
Joined: 10 Jul 2019
Last visit: 06 Apr 2025
Posts: 1,353
Own Kudos:
705
 [1]
Given Kudos: 1,658
Posts: 1,353
Kudos: 705
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Since the question asks for a Ratio answer, we can use some values in line with the given information in order to make the work easier.


Let speed of R = 4 m/s

Speed of A = 5 m/s


R gets a head start for some time and then A leaves after R is X meters in front.

They then both run for 20 seconds.

After this time, A is in front of R by X meters

Using our chosen numbers:

In 20 seconds:

A covered distance = (5) (20) = 100 m
R covered distance = (4) (20) = 80 m

This means R manages to run for 10 m before A started and then fell behind another 10 m (X and X).


Over the constant distance of the entire race, the ratio of the speeds will be inversely proportional to the time taken.

Speed of A to Speed of R = 5 : 4

Time A to finish race : Time R to finish race = 4x : 5x

Since R takes 60 seconds ——-> A would take 48 seconds to finish the race.

At our assume speed of R = 5 m/s ———> this would make the race distance = (5) (48) = 240


Lastly, we need to know how much distance A covered when he passed R.

From above, based on our chosen numbers, R starts off with a 10 m head start. Then A leaves.

Same direction Relative Speed = 5 - 4 = 1 meter per second

Every 1 second, A catches up 1 meter.

Thus, it will take A 10 seconds to catch up the 10 meters.

For this travel time, running at a speed of 5 m/s———> A will have traveled a distance = (5) (10) = 50 m when he passes R


From above, total distance of race was 240 m

Fraction of race A covers when he passes R = 50/240 = 5/24

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,349
Own Kudos:
Posts: 37,349
Kudos: 1,008
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:
Math Expert
102592 posts
PS Forum Moderator
679 posts