Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How would I write a summation for the average speed of an object, given $10$ speeds (which were calculated $r=\frac{d}{t}$)? Would it be:

$$ \sum_{i = 1}^{10} \frac{d_i}{t_i}$$

or am I wrong? I'm not sure about the subscript i's after distance and time, and if they are actually number sequences that I could use. Thanks.

share|improve this question
add comment

2 Answers 2

up vote 2 down vote accepted

No. Generally average speed is defined as the total distance divided by the total time. That would be

$$ \frac{\sum_{i = 1}^{10} d_i}{\sum_{j = 1}^{10} t_j} $$

share|improve this answer
add comment

This type of thing leads to some amusing puzzles. Like if you take a trip and for the first half you go 30 mph and for the last half you go 70 mph, is your average speed 50 mph? Answer: depends what you mean by half. If "half" means half of the time, then the answer is yes, but if "half" means half of the distance, then the answer is no.

Similarly: if you average 30 mph on an outbound trip, how fast do you have to go on the return trip in order to average 60 mph for the whole trip?

Similarly: construct a scenario where there are two baseball players, and on each day player 1 has a higher batting average than player 2, but after a week player 2 has a higher (cumulative) average than player 1.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.