Last visit was: 19 Jun 2025, 02:55 It is currently 19 Jun 2025, 02:55
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
EnterMatrix
Joined: 22 Mar 2010
Last visit: 18 Aug 2010
Posts: 35
Own Kudos:
238
 [74]
Given Kudos: 1
Posts: 35
Kudos: 238
 [74]
3
Kudos
Add Kudos
70
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 June 2025
Posts: 102,138
Own Kudos:
Given Kudos: 93,936
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,138
Kudos: 733,590
 [26]
11
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
User avatar
temp33
Joined: 20 Jul 2010
Last visit: 19 Aug 2010
Posts: 55
Own Kudos:
353
 [14]
Given Kudos: 7
Concentration: Finance, Business Consulting
 Q44  V25 GMAT 2: 600  Q50  V22
Posts: 55
Kudos: 353
 [14]
7
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
General Discussion
avatar
meshtrap
Joined: 26 Mar 2010
Last visit: 04 Nov 2010
Posts: 5
Own Kudos:
15
 [5]
Given Kudos: 9
Posts: 5
Kudos: 15
 [5]
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

It is pretty involuntary to come up with 35 miles per hour as the average speed in this case. But, that is wrong. Since, the car has taken more time to travel at 30 mph and less time to travel at 40 mph, the avg speed of the car would be somewhere between 30 and 35(mean) and closer to 35. If I had no time on my hands and had to make a calculated guess, I would have chosen C.

The correct way to find the avg speed is to calculate the total distance and the total time and divide the total distance by total time.

Let the one way distance in this case be D. So the total distance is 2D(travelled over the same route twice)

Total Time = Time taken to travel distance D at 30 mph + time taken to travel distance D at 40 mph
= \((D/30) + (D/40)\)
= \(7D/120\)
Thus avg speed = Total distance/total time
= \((2D)/(7D/120)\)
= 34.285

Hope it helps,
meshtrap
User avatar
zxcvbnmas
Joined: 06 Jun 2014
Last visit: 22 Oct 2016
Posts: 71
Own Kudos:
622
 [1]
Given Kudos: 109
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47
GMAT 1: 450 Q27 V21
Posts: 71
Kudos: 622
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
We can pick any number for distance that is divisible by both 30 and 40. Since we have rate and distance, by plugging in the rate formula (r=d/t) we can solve for the average rate/speed
    City``` Rate--- Time ---Distance
    M-R.... 30--- 4 ---- 120
    R-M ... 40 --- 3 ---- 120
    Total 34.28 --- 7 ---- 240
34.28 ~ 34.3
User avatar
Nunuboy1994
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 559
Own Kudos:
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 559
Kudos: 122
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

This is just an approximation and round trip problem- we simply pick a value- which is usually the LCM

Total Distance= Avgspeed * Total Time

120/30= 4
120/40= 3

240= average speed * 7

240/7= 34.3
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,757
Own Kudos:
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,757
Kudos: 33,874
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

A) 32.0
B) 33.0
C) 34.3
D) 35.5
E) 36.5

APPROACH #1: Apply the average speed formula
Average speed formula = (total distance travelled)/(total travel time)
If we let d = the distance from Mayville to Rome, then total distance travelled = 2d (since the car traveled from Mayville to Rome and then back)

time = distance/rate
So, the travel time from Mayville to Rome = d/30
Similarly, the travel time from Rome to Mayville = d/40
So, the total travel time = d/30 + d/40 = 4d/120 + 3d/120 = 7d/120

The average speed for the round trip= (2d)/(7d/120)
= (2d)(120/7d)
= 240d/7d
= 240/7 = 34 2/7 ≈ 34.3
Answer: C

APPROACH #2: Assign a "nice" distance between Mayville and Rome
So, let's say the distance between Mayville and Rome = 120 miles - since this distance that works well with 30 miles per hour AND 40 miles per hour

Time = distance/speed
So, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours
Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours

Average speed = (total distance traveled)/(total time)
= (120 + 120)/(4 + 3)
= 240/7 = 34 2/7 ≈ 34.3
Answer: C

Cheers.
Brent
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,003
Own Kudos:
7,854
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 3,003
Kudos: 7,854
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

We can use the average rate formula: average = total distance/total time, and let the distance each way = 120 miles. (Note that we could use any number for the distance, but we have chosen the convenient number 120 because it is evenly divisible by both 30 and 40, making the arithmetic easier.)
average = 240/(120/30 + 120/40)

average = 240/(4 + 3) = 240/7 = 34.3

Answer: C
User avatar
AkshdeepS
Joined: 13 Apr 2013
Last visit: 18 Jun 2025
Posts: 1,442
Own Kudos:
1,806
 [1]
Given Kudos: 1,001
Status:It's near - I can see.
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Products:
Posts: 1,442
Kudos: 1,806
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Total distance = D + D = 2D

Total time = D/30 +D/40

Avg. Speed = Total distance / Total time

Avg. Speed =\(\frac{(2D)}{(D/30 + D/40)}\)

Avg. Speed = \(\frac{240D}{70D}\)

Avg. Speed = 34.2 approx

Hence (C)
User avatar
epiphany1
Joined: 11 Aug 2018
Last visit: 30 Jan 2021
Posts: 87
Own Kudos:
Given Kudos: 210
Posts: 87
Kudos: 71
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For Avg speed if two speeds are given formula is Avg speed=2*S1*S2/S1+S2=34.2
avatar
tsimo1000
Joined: 20 Jan 2019
Last visit: 30 Jun 2024
Posts: 6
Own Kudos:
Given Kudos: 155
Posts: 6
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AkshdeepS
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Total distance = D + D = 2D

Total time = D/30 +D/40

Avg. Speed = Total distance / Total time

Avg. Speed =\(\frac{(2D)}{(D/30 + D/40)}\)

Avg. Speed = \(\frac{240D}{70D}\)

Avg. Speed = 34.2 approx

Hence (C)

can you please explain how you reached to Avg. Speed = \(\frac{240D}{70D}\) ?
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 18 Jun 2025
Posts: 1,853
Own Kudos:
Given Kudos: 707
Location: India
Posts: 1,853
Kudos: 7,733
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If the distance is equal in both trips, then
Average speed =2xy/(x+y)
=2*30*40/70
=34.3 miles/hr
x=speed in first trip
y= speed in second trip
User avatar
rishab0507
Joined: 12 Mar 2019
Last visit: 25 Feb 2021
Posts: 181
Own Kudos:
Given Kudos: 105
Posts: 181
Kudos: 106
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Straight formula : If distance is same and different speeds.

Av speed: 2* 1/ (1/30 +1/40)
LCM of 30 and 40 is 120

2* 1/(4/120 +3/120)
2*120 /7 = 240/7 : 34.3

Answer :C
User avatar
EatMyDosa
Joined: 06 Jan 2017
Last visit: 01 Dec 2022
Posts: 85
Own Kudos:
Given Kudos: 283
Location: India
Concentration: General Management, Finance
GPA: 3.33
Products:
Posts: 85
Kudos: 109
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

A. 32.0
B. 33.0
C. 34.3
D. 35.5
E. 36.5

Hi VeritasKarishma,

I tried to solve this question using your weighted average method (below) and got a different answer. Could you please help me figure out why the method did not work in this case?

V1/V2 = 40-x/x-30 ----------- where x = average speed

30/40 = 40-x/x-30

on solving further, we get

x = 250/7 = 35.7 (this is in fact none of the options given)
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,082
Own Kudos:
18,654
 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,082
Kudos: 18,654
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Average speed (when distance is same / constant) = \(\frac{{2 * a * b} }{ {a + b}}\)

=> Average speed = \(\frac{{2 * 30 * 40} }{ {30 + 40}}\)

=> Average speed = \(\frac{{2 * 30 * 40} }{ {70}}\)

=> Average speed = 34.28 ≈ 34.3

Answer C
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 19 Jun 2025
Posts: 16,058
Own Kudos:
Given Kudos: 472
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,058
Kudos: 73,774
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EatMyDosa
EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?

A. 32.0
B. 33.0
C. 34.3
D. 35.5
E. 36.5

Hi VeritasKarishma,

I tried to solve this question using your weighted average method (below) and got a different answer. Could you please help me figure out why the method did not work in this case?

V1/V2 = 40-x/x-30 ----------- where x = average speed

30/40 = 40-x/x-30

on solving further, we get

x = 250/7 = 35.7 (this is in fact none of the options given)

What are V1 and V2 in your equation?
The weight when averaging speeds is time taken. Since the distance is the same in the two cases, the time taken would be in the ratio of inverse of speeds i.e. 4:3.

4/3 = 40-x/x-30
x = 34.3 mph

Check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/1 ... -averages/
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 19 June 2025
Posts: 5,613
Own Kudos:
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,613
Kudos: 5,100
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour.
Asked: Of the following, which is closest to the average speed, in miles per hour, for the round trip?

Total distance = 2x
Total time = x/30 + x/40 = 7x/120

Average speed = 2x*120/7x = 240/7 = 34.3

IMO C
User avatar
Schachfreizeit
Joined: 17 Nov 2022
Last visit: 02 Feb 2023
Posts: 111
Own Kudos:
Given Kudos: 8
Posts: 111
Kudos: 8
Kudos
Add Kudos
Bookmarks
Bookmark this Post
temp33
IMO C

EnterMatrix
A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
○ 32.0
○ 33.0
○ 34.3
○ 35.5
○ 36.5

Solution:

Average speed for the entire trip = 2uv/(u+v),
where u = speed of going
v = speed of returning


Thus, average speed = 2*40*30/(70) = 34.3 mi/h

Hence, C


what kind of formula is this?
User avatar
egmat
User avatar
e-GMAT Representative
Joined: 02 Nov 2011
Last visit: 19 Jun 2025
Posts: 4,597
Own Kudos:
Given Kudos: 683
GMAT Date: 08-19-2020
Expert
Expert reply
Posts: 4,597
Kudos: 32,277
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Schachfreizeit
temp33
IMO C


Average speed for the entire trip = 2uv/(u+v),
where u = speed of going
v = speed of returning


Thus, average speed = 2*40*30/(70) = 34.3 mi/h

Hence, C


what kind of formula is this?

Hi Schachfreizeit,
Thanks for your query.

The formula you are asking about is the simplified version of the average speed formula for a round trip. Let me show you how!

Please go through the explanation below, where I used a hypothetical situation to derive the formula of the average speed you are confused about. I will only use the definition of average speed.


DERIVATION:

Suppose the distance between two random points - point A and point B - is ‘d’ meters. A car moves from A to B at a speed of ‘u’ miles/hour and then returns from B to A at a speed of ‘v’ miles/hour. We need to find the average speed for this round trip by car A.

Now, by the definition of average speed, we know that:

Average speed = \(\frac{Total distance}{Total time}\) …(I)

Let’s try to find the numerator and denominator separately, using information from our hypothetical situation.
  • Total distance covered by the car = d (from A to B) + d (from B to A) = 2d …(II)
  • Total time taken= Time taken from A to B + Time taken from B to A
      = \(\frac{distance}{speed}\)(From A to B) + \(\frac{distance}{speed}\)(From B to A)
      =\(\frac{d}{u}+\frac{d}{v}\) = \(\frac{(dv + du)}{uv}\) = \(\frac{d(v + u)}{uv}\) …(III)

So, using the values of total distance and total time from (II) and (III) into (I), we get
  • Average speed = \(\frac{2d}{{d(u+v)/uv}}\)= \(\frac{2duv}{d(u+v)}\)=\(\frac{2uv}{(u+v)}\)


And see! This is the formula you were looking for.


APPLICATION OF THE FORMULA:
Let me again show you how this formula can be directly used to solve our question:

Here, we have u = 30 miles per hour and v = 40 miles per hour. Using these values in the formula we derived, we get:
  • Average speed = \(\frac{2(30)(40)}{(30+40)}\)= 34.28 miles per hour


TAKEAWAY:
Whenever speed for to journey and back journey is given, where the distances in both legs of the journey are identical, we can directly use the following formula to find average speed.
  • Average speed = \(\frac{2uv}{u+v}\), where u, v are the speeds of the “to” and “back” journeys, respectively.


Hope this helps!


Best,
Aditi Gupta
Quant Expert, e-GMAT
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,230
Own Kudos:
Posts: 37,230
Kudos: 1,001
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
102138 posts
PS Forum Moderator
648 posts