BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Two methods to calculate total average speed

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 50
Joined: Thu Oct 04, 2007 12:26 pmFollowed by: 3 members
Location: RTP, NC
Thanked: 26 times
by achandwa » Tue Nov 13, 2007 7:31 am
In problems that ask you to calculate total average speed, given the speed for onward and return trip, you could apply a formula or a neat trick to get to the answer faster. Lets derive the genral formula first and see how it applies it to couple of examples.

Say, a car travels at S1 mph on a trip and at S2 mph on return trip. What is its average speed for the entire trip?
Solution:
*** Don't fall in the trap of just averaging the 2 speeds. Overall average speed is not (S1+S2)/2. ***
Total average speed is simply = Total distance/Total time
Lets say,
D = distance travelled by the car in EACH direction
t1 = time spent on onward trip
t2 = time spent on return trip
Thus, the total distance travelled by the car = D+D= 2D
And, by the formula, Speed = Distance/Time
S1 = D/t1 => t1 = D/S1
S2 = D/t2 => t2 = D/S2
Total average speed = Total Distance/Total time = 2D/(t1+t2) = 2D/(D/S1+D/S2) = 2S1*S2/(S1+S2)

Remember this general formula for a total average speed problems:
Total average speed = 2S1*S2/(S1+S2)

Example:
A car travels at 60 mph on a trip and at 100 mph on return trip. What was its average speed for the entire trip?
Solution:
*** Total average speed is not (60+100)/2 = 80 ***
Total average speed = 2*60*100/(100+60) = 2*60*100/160 = 2*60*5/8 = 60*5/4 = 15*5 = 75

Alternatively, you may want to check if the following trick saves you some time.
Calculate the ratio of the speeds r1:r2. In our example it is 60:100 = 3:5
Then divide the difference between the speeds (s2-s1) by r1+r2 to get one part. In our example (100-60)/(3+5) = 5 is one part
The required answer is r1 parts away from the lower speed. That is, 60+r1*5 = 60+3*5 = 75 mph

Lets check how it works for S1=20 mph and S2=40 mph
Method 1:
Using the formula Total avg speed = 2S1*S2/(s1+s2)
= 2*20*40/(20+40)
= 2*20*40/60
= 80/3 = 26.67 mph
Method 2:
Ratio r1:r2 = 20:40 = 1:2
r1+r2 = 3
1 part = (S2-S1)/(r1+r2) = (40-20)/3 = 20/3 = 6.67
Total Avg speed is r1 parts away from smaller speed
Therefore avg speed = 20+ r1*6.67 = 20+1*6.67 = 26.67 mph


Hope you find this useful.
-Ashish
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Quantitative Reasoning |

GMAT/MBA Expert

User avatar
Site Admin
Posts: 6778
Joined: Mon Feb 13, 2006 8:30 amFollowed by: 994 members
Location: Los Angeles, CA
Thanked: 1249 times

by beatthegmat » Tue Nov 13, 2007 10:39 pm
This is really great Ashish! I'm adding this to the Beat The GMAT del.icio.us.
Beat The GMAT | The MBA Social Network
Community Management Team

Research Top GMAT Prep Courses:
https://www.beatthegmat.com/gmat-prep-courses

Research The World's Top MBA Programs:
https://www.beatthegmat.com/mba/school
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sun Jan 06, 2008 3:01 pm

Re: Two methods to calculate total average speed

by butler » Sun Jan 27, 2008 3:38 pm
Can you explain how this works? 2D/(D/S1+D/S2) = 2S1*S2/(S1+S2)

Thank you
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sun Jan 27, 2008 10:13 pm
Location: North Vancouver, BC, Canada
Thanked: 1 times

Re: Two methods to calculate total average speed

by gfinlay » Sat Feb 16, 2008 1:29 pm
butler wrote:Can you explain how this works? 2D/(D/S1+D/S2) = 2S1*S2/(S1+S2)
To simplify the fractions in the formula, you need to multiply the numerator and denominator by the same value (remember that multiplying by X/X = 1 retains the value of the expression). In the case of the formula above, we need to multiply top and bottom by S1*S2 (common denominator for the fractions D/S1 and D/S2).
So here is the derivation, not leaving out any steps...

2 * D / (D/S1 + D/S2)
Multiply top and bottom by S1 * S2
= 2 * D * S1 * S2 / ((D/S1 + D/S2) * S1 * S2)
Distribute the multipliers in the denominator
= 2 * D * S1 * S2 / (D * S2 + D * S1)
Factor out the D from the denominator (distributive law)
= 2 * D * S1 * S2 / D (S2 + S1)
Cancel the D factor from top and bottom
= 2 * S1 * S2 / (S2 + S1)
Addition is of course commutative, so the order of the terms in the denominator can be reversed ...
= 2 * S1 * S2 / (S1 + S2)

Of course it saves time to just memorize the formula so that you don't have to derive it unless you forget. However, recognize the danger of applying the formula to a distance/speed/time question that doesn't exactly match this pattern (for what is asked).

I hope this helps. If you need more practice on simplification and you happen to have the Princeton Review "Cracking the GMAT 2008 edition", I suggest you go through the Fractions section on pp. 77-81. Remember that in algebra, the rules for arithimetic operations (associative law, commutative law, distributive law, etc) are the same with variables as they are for number constants.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Fri Sep 14, 2007 7:34 am
Thanked: 1 times
GMAT Score:650

One point

by landroni » Thu Oct 16, 2008 1:04 am
I wanted to stress one point (idea taken from this Math Review).

Since we're on to averaging speeds, the speeds will be different in all the cases.
achandwa wrote:Say, a car travels at S1 mph on a trip and at S2 mph on return trip. What is its average speed for the entire trip?

Remember this general formula for a total average speed problems:
Total average speed = 2S1*S2/(S1+S2)
This is the harmonic mean. This formula applies when the situation is:
- same distance (onward and return trip)

As long as you're in a `same or equal distances' situation, any information on time is pretty much irrelevant.
achandwa wrote:*** Don't fall in the trap of just averaging the 2 speeds. Overall average speed is not (S1+S2)/2. ***
You would use the weighted arithmetic mean when the situation is:
- different distance
- different time

The `time' is the frequency, or weight factor. You would use the simple arithmetic mean in a simplified situation:
- different distance
- same time

The `time' weight factor has no impact on the average formula, since it factors itself out.

Liviu
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 140
Joined: Sat Feb 28, 2009 8:51 amFollowed by: 3 members
Location: India
Thanked: 14 times

Re: Two methods to calculate total average speed

by farooq » Wed Oct 28, 2009 5:48 am
A man walks by speed 2 KM/hr and cover 3/4 of total distance in 10 minutes and reaming distance in 30 minutes. What is the total distance ?

A. 400
B. 4.80
C. 360
D. 40
E. None
Regards,
Farooq Farooqui.
London. UK

It is your Attitude, not your Aptitude, that determines your Altitude.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 177
Joined: Thu Aug 14, 2008 11:59 am
Thanked: 25 times

by mp2437 » Wed Oct 28, 2009 6:53 am
I say choice E. I am getting an answer of 4/9 km.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Mon Mar 01, 2010 3:03 pm

by hkyoon » Sun Mar 28, 2010 5:07 pm
Yes, I do too

2km/hr * 1/6 hr = 3/4 * Total Distance
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member
Thanked: 32 times

Two methods to calculate total average speed

by eaakbari » Tue Mar 30, 2010 6:39 am
Well its obviously E. How can a man take longer for 1/4th the distance than 3/4th of it

And great contribution Ashish. That sure was informative.
Just as an add on, I have attached for 3 speeds or greater too. Check it out
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Tue Jun 29, 2010 8:17 am

by dhruv pillai » Tue Jun 29, 2010 8:29 am
achandwa wrote:In problems that ask you to calculate total average speed, given the speed for onward and return trip, you could apply a formula or a neat trick to get to the answer faster. Lets derive the genral formula first and see how it applies it to couple of examples.

Say, a car travels at S1 mph on a trip and at S2 mph on return trip. What is its average speed for the entire trip?
Solution:
*** Don't fall in the trap of just averaging the 2 speeds. Overall average speed is not (S1+S2)/2. ***
Total average speed is simply = Total distance/Total time
Lets say,
D = distance travelled by the car in EACH direction
t1 = time spent on onward trip
t2 = time spent on return trip
Thus, the total distance travelled by the car = D+D= 2D
And, by the formula, Speed = Distance/Time
S1 = D/t1 => t1 = D/S1
S2 = D/t2 => t2 = D/S2
Total average speed = Total Distance/Total time = 2D/(t1+t2) = 2D/(D/S1+D/S2) = 2S1*S2/(S1+S2)

Remember this general formula for a total average speed problems:
Total average speed = 2S1*S2/(S1+S2)

Example:
A car travels at 60 mph on a trip and at 100 mph on return trip. What was its average speed for the entire trip?
Solution:
*** Total average speed is not (60+100)/2 = 80 ***
Total average speed = 2*60*100/(100+60) = 2*60*100/160 = 2*60*5/8 = 60*5/4 = 15*5 = 75

Alternatively, you may want to check if the following trick saves you some time.
Calculate the ratio of the speeds r1:r2. In our example it is 60:100 = 3:5
Then divide the difference between the speeds (s2-s1) by r1+r2 to get one part. In our example (100-60)/(3+5) = 5 is one part
The required answer is r1 parts away from the lower speed. That is, 60+r1*5 = 60+3*5 = 75 mph

Lets check how it works for S1=20 mph and S2=40 mph
Method 1:
Using the formula Total avg speed = 2S1*S2/(s1+s2)
= 2*20*40/(20+40)
= 2*20*40/60
= 80/3 = 26.67 mph
Method 2:
Ratio r1:r2 = 20:40 = 1:2
r1+r2 = 3
1 part = (S2-S1)/(r1+r2) = (40-20)/3 = 20/3 = 6.67
Total Avg speed is r1 parts away from smaller speed
Therefore avg speed = 20+ r1*6.67 = 20+1*6.67 = 26.67 mph


Hope you find this useful.
-Ashish
thank you Mr Ashish
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Wed Nov 17, 2010 12:49 am

by peertje888 » Wed Nov 17, 2010 1:17 am
To see if it made any difference calculating the average wind speed of a turbine I made a test in Excel. In this scenario the duration for every bin is the same. That is why it didn't make any difference.
Attachments
TotalAverage.xlsx
(9.24 KiB) Downloaded 469 times
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Fri Apr 29, 2011 10:11 am

by Uvin » Fri Apr 29, 2011 10:14 am
a object travels on a strait line has V1 velocity for half of its journey. For the rest, it gets V2 velocity for the first half of the rest, and then V2 velocity for the other half. What is the average speed of the object ?
Can anybody help me with this question???
thank you!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Thu Apr 28, 2011 12:45 am
Thanked: 1 times

by tapanu » Wed May 04, 2011 5:15 am
Thanks Ashish !!!
Very helpful !!
The will to win is worthless if you do not have the will to prepare.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sun Jul 03, 2011 8:33 pm
Thanked: 1 times

by ajaygiri » Tue Jul 12, 2011 2:22 pm
thank you ashish!

could not follow the ratio logic though, but the first one is crystal. thanks for the lucid explanation.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 82
Joined: Fri Nov 04, 2011 12:35 amFollowed by: 2 members

by amit28it » Sat Dec 24, 2011 3:43 am
achandwa wrote:In problems that ask you to calculate total average speed, given the speed for onward and return trip, you could apply a formula or a neat trick to get to the answer faster. Lets derive the genral formula first and see how it applies it to couple of examples.

Say, a car travels at S1 mph on a trip and at S2 mph on return trip. What is its average speed for the entire trip?
Solution:
*** Don't fall in the trap of just averaging the 2 speeds. Overall average speed is not (S1+S2)/2. ***
Total average speed is simply = Total distance/Total time
Lets say,
D = distance travelled by the car in EACH direction
t1 = time spent on onward trip
t2 = time spent on return trip
Thus, the total distance travelled by the car = D+D= 2D
And, by the formula, Speed = Distance/Time
S1 = D/t1 => t1 = D/S1
S2 = D/t2 => t2 = D/S2
Total average speed = Total Distance/Total time = 2D/(t1+t2) = 2D/(D/S1+D/S2) = 2S1*S2/(S1+S2)

Remember this general formula for a total average speed problems:
Total average speed = 2S1*S2/(S1+S2)

Example:
A car travels at 60 mph on a trip and at 100 mph on return trip. What was its average speed for the entire trip?
Solution:
*** Total average speed is not (60+100)/2 = 80 ***
Total average speed = 2*60*100/(100+60) = 2*60*100/160 = 2*60*5/8 = 60*5/4 = 15*5 = 75

Alternatively, you may want to check if the following trick saves you some time.
Calculate the ratio of the speeds r1:r2. In our example it is 60:100 = 3:5
Then divide the difference between the speeds (s2-s1) by r1+r2 to get one part. In our example (100-60)/(3+5) = 5 is one part
The required answer is r1 parts away from the lower speed. That is, 60+r1*5 = 60+3*5 = 75 mph

Lets check how it works for S1=20 mph and S2=40 mph
Method 1:
Using the formula Total avg speed = 2S1*S2/(s1+s2)
= 2*20*40/(20+40)
= 2*20*40/60
= 80/3 = 26.67 mph
Method 2:
Ratio r1:r2 = 20:40 = 1:2
r1+r2 = 3
1 part = (S2-S1)/(r1+r2) = (40-20)/3 = 20/3 = 6.67
Total Avg speed is r1 parts away from smaller speed
Therefore avg speed = 20+ r1*6.67 = 20+1*6.67 = 26.67 mph


Hope you find this useful.
-Ashish
Yes Ashish it was really helpful .I was also having the same doubt in this question .It was not exactly same as it is .But in my question there is same logic as in this question .So i was able to solve my question and is able to know how to simplify ratios .Thanks for your support .
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply