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# Average Speed on GMAT

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Intern
Joined: 25 Sep 2012
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Concentration: General Management
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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]

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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:
E

See if you can apply that knowledge to this question.
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Re: Average Speed on GMAT [#permalink]

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20 Dec 2013, 04:20
I have a question.

Suppose A travels 40 miles at an average speed of 40 mph, waits for 10 minutes and travels back on the same route at an average speed of 30 mph. What is A's average speed for the entire trip?

Formula = Total Distance / Total Time

We know the total distance is 40 miles. While calculating the total time, should we add the waiting time or not?
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Re: Average Speed on GMAT [#permalink]

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23 Dec 2013, 22:03
aakrity,

To tackle average speed problems it is best to stick to the definition of average speed, which is the total distance traveled divided by the total time spent on the trip. In the example you listed, you would be using the total time taken on the trip which would include the 10 minute waiting period.

Cheers,
Dabral
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Re: Average Speed on GMAT [#permalink]

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16 Nov 2014, 21:37
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Expert's post
GMATPill wrote:

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:
E

Responding to a pm:
Solving this using weighted averages.

When talking about speeds, what are the weights? The weight given to each speed is the time for which that speed was maintained.

Cavg = (C1*w1 + C2*w2)/(w1 + w2)
Avg Speed = (Speed1*Time1 + Speed2*Time2)/(Time 1 + Time2)
Avg Speed = (Distance1 + Distance2)/(Time 1 + Time2)
Avg Speed = Total Distance/Total Time

So the weighted avg also ultimately boils down to this simple formula only.

Distance traveled cannot be the weight.

Avg Speed = (Speed1*Distance1 + Speed2*Distance2)/(Distance1 + Distance2) makes no physical sense.

Since this question gives you the fraction of distance, you will need to convert it to time to use weighted avgs. Easier would be to use Total Distance/Total Time

Say total distance is D

Time taken 1 = Distance1/Speed1 $$= \frac{(x% of D)}{40} = \frac{xD}{4000}$$
Time taken 2 = Distance2/Speed2 $$= \frac{[(1 - x%) of D]}{60} = \frac{(100-x)D}{6000}$$

Avg Speed = Total Distance/Total Time $$= \frac{D}{\frac{xD}{4000} + \frac{(100-x)D}{6000}} = \frac{12000}{200+x}$$

Another way to deal with this question would be to plug in values in the options.
When you put x = 100, you should get the avg speed as 40 (entire distance traveled at 40 mph)
When you put x = 0, you should get the avg speed as 60 (entire distance traveled at 60 mph)

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

C. (300-x)/5 --------- When you put x = 50 here, you get avg speed = 50. This is not correct. Avg speed will be 50 only when time taken in both cases is equal. Here distance traveled in both cases will be equal. When you put x = 50, you should get avg speed = 48 (When distance traveled is the same, avg speed = 2ab/(a+b) = 2*40*60/(40+60) = 48)

Answer must be (E) by elimination.
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Re: Average Speed on GMAT   [#permalink] 16 Nov 2014, 21:37
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