SDW2 wrote:
Bunuel wrote:
If Car A took n hours to travel 2 miles and Car B took m hours to travel 3 miles, which of the following expresses the time it would take Car C, traveling at the average (arithmetic mean) of those rates, to travel 5 miles?
A. \(\frac{10nm}{3n + 2m}\)
B. \(\frac{3n + 2m}{10(n + m)}\)
C. \(\frac{2n + 3m}{5nm}\)
D. \(\frac{10(n + m)}{2n + 3m}\)
E. \(\frac{5(n + m)}{2n + 3m}\)
PS78502.01
Quantitative Review 2020 NEW QUESTION
Hello,
Can any math expert please tell me why the average rate here is not calculated as total distance/ total time taken= (3+2)/(m+n)= 5/(m+n) ?
Because in this question (A plane traveled k miles in its first 96 minutes of flight time. If it completed the remaining 300 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?) avg speed is calculated using the method I just mentioned.
So how are these two questions different in terms of only calculating avg speed (if at all they're)?
PS- I couldn't post the link since I am a new member here but you can search this question on the forum.
Hoping to get some clarity on this concept.
VeritasKarishma BunuelIt's an interesting point and hence, I will add my two cents too (though Ian has already explained it very well).
Normally, average speed is the weighted average of two or more speeds when time is the weight. It is also Total Distance/Total Time.
So average speed of a car that travels 2 miles in m hrs and 3 miles in n hrs will be 5/(m + n).
It will also be [(2/m)*m + (3/n)*n] / (m + n) = 5/(m+n) (Using weighted average concept)
They both match and of course they should. Note that this concept of Total distance/Total time makes sense for one car.
The question here is different. Here, you are given the rates of two cars and are asked to find their arithmetic mean (We use arithmetic mean only when time for which they travel is the same but the cars here travel for diff times, m and n hrs).
Hence, we find their rates and find the AM
[(2/m) + (3/n)] / 2
We do not take the weighted average as shown above because we have been asked to take the arithmetic mean of the rates.
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