Average Speed on GMAT

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Average Speed on GMAT [#permalink]

08 Oct 2012, 05:09

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Hi Folks,

The purpose of this post is to clarify the concept of average speed, which is not equal to the average of two speeds.
Basic Formula : Distance=Speed*Time
D=T*S

Average Speed= Total Distance/Total time taken

Say, a body covers distance D in two parts. D=d1+d2
d1 distance at an average speed s1
and
d2 distance at an average speed s2
(using T=D/S)
We know that Average Speed = [d1+d2][/t1+t2]
Therefore we need to calculate the time taken for each fraction of journey :

time taken to cover d1,say t1 = d1/s1

time taken to cover d1,say t2 = d2/s2

Average Speed= [d1+d2][/d1/s1+d2/s2]

Simplifying :

Average Speed = [d1+d2]*s1*s1/ (s1*d2+s2*d1)

Specific Case :

For round Trips : d1=d2=d

the formula reduces to :: Average Speed = (2d*s1*s2)/(s1*d+s2*d)
= 2(s1*s2)/(s1+s2)
* for round trips, if we are given the speeds, we do not need the total distance to calculate the Avg Speed.

**If anyone can, please do post the questions on this topic.
Hope that Helps!!

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Re: Average Speed on GMAT [#permalink]

17 Oct 2012, 15:03

That's right, you can't necessarily take the average of two speeds - you can only do that if the time weighted for each of those two speeds is the same. So if you go for 1 hour at 40mph and 1 hour at 60mph, then the average will be 50mph.

However, if you travel 1 hour at 40mph and only 30 minutes at 60mph, the average is NOT (40+60)/2 = 50mph
Instead, average total speed is equal to total distance divided by total time.

Total distance = 40mph x 1 hour + 60mph *0.5hour = 70miles
Time = 1.5hr

Average speed = 70miles / 1.5hr = 46.7mph (NOT 50mph)

So one example of a question is OG12 #149

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

A. (180-x)/2
B. (x+60)/4
C. (300-x)/5
D. 600/(115-x)
E. 12,000/(x+200)

[Reveal] Spoiler:

See if you can apply that knowledge to this question.
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Re: Average Speed on GMAT [#permalink] 17 Oct 2012, 15:03

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