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Average Speed Formulas-- Need Help!

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Average Speed Formulas-- Need Help! [#permalink] New post 19 Jan 2011, 06:14
I know that average speed = total distance / total time

But can someone explain another formula I've found on this site:

average speed = (2ab)/(a+b)
a and b represent the average speed of each trip

Where does this come from?

Thanks!
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Re: Average Speed Formulas-- Need Help! [#permalink] New post 19 Jan 2011, 07:19
suesie970 wrote:
I know that average speed = total distance / total time

But can someone explain another formula I've found on this site:

average speed = (2ab)/(a+b)
a and b represent the average speed of each trip

Where does this come from?

Thanks!


Hey,

This formula is applicable when distances are equal.
example;
Mack travels half of his journey by train at the speed f 120 km/h ad rest half by car at 80 km/h. what is the average speed?
We can solve this problem by many ways.
1. Total distance,take LCM of 120 and 80 =240
therefore,time taken by train=120/120= 1 h
time taken by car = 120/80 = 3/2 h
Average speed = total distance/total time taken
=240/1+3/2
= 96 km/h

2.Method ;
Average speed=2xy/x+y ,where x and y are the speeds
Average speed= 2*120*80/120+80
= 96 km/h

I hope it helps you.
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Re: Average Speed Formulas-- Need Help! [#permalink] New post 19 Jan 2011, 18:27
SoniaSaini,
Thanks for taking the time to respond. I understand how to use the formulas, I just would like to know where the second one comes from. That is, how was it derived?
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Re: Average Speed Formulas-- Need Help! [#permalink] New post 25 Feb 2012, 08:52
suesie the formula you are referring to - 2ab/(a+b) is derived from Harmonic mean.. As we know that average speed of two speed S1 and S2 is not a AM.. But interestingly it's HM.. So if a vehicle moves with a speed of S1 and S2, covering same distance(you need to be sure of this to apply the HM formula) then you can quickly use the HM formula i.e. 2ab/(a+b)
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Re: Average Speed Formulas-- Need Help! [#permalink] New post 18 Jun 2013, 03:24
SoniaSaini wrote:
suesie970 wrote:
I know that average speed = total distance / total time

But can someone explain another formula I've found on this site:

average speed = (2ab)/(a+b)
a and b represent the average speed of each trip

Where does this come from?

Thanks!


Hi Sonia,

Say, I have traveled a distance of 'X' in 'A' kmph and 'Y' in 'B' kmph respectively.

I now have two 'time' values i.e.
X/A---------------(1)
Y/B---------------(2)

Total distance traveled by me = X+Y

Total time taken by me (1)+(2)

i.e. (BX+AY)/(AB)-----------------------------------------*/ I took the LCM /*

Avg Speed = Total distance traveled by me / Total time taken by me

= X+Y / (BX+AY)/(AB)

= (X+Y)AB / (AY+BX)-----------------------------/This is the final formula to find average speed if the distances are different i.e. X<>Y [X is not equal to Y] /

If X=Y

Average speed = (2X)(AB) / (AX+BX) = 2AB/(A+B) ----------------- /Formula of finding average if X=Y/
Re: Average Speed Formulas-- Need Help!   [#permalink] 18 Jun 2013, 03:24
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