/sci/, this is frustrating me. Help me out.
Let's say I travel 10 miles at 20 mph - that takes 0.5 hrs.
Now let's say I travel half the distance at 15 mph and the other half at 25 mph. That comes out at 0.5333 hrs.
My question is, why don't they both take 0.5 hrs. Why doesn't travelling 5 mph faster the last half of the distance make up for travelling 5 mph slower the first half of the distance?
You're looking at average speed over distance, while you should be looking at average speed over time. The average speed over distance is indeed 20mph (you travel equal distances 15 and 25 mph), but the average speed over time is lower.
The reason it's lower is because you spend less time traveling 25 mph, since it takes less time to cover the 5 miles. So the last half where you're travelling faster can't make up for the first half where you're travelling slower. Lower average speed means a longer travel time, hence the 0.5333 hrs you came up with.
The distance travelled is equal to the average velocity (over the entire trip), multiplied by the time. Since it takes longer to travel 5 miles at 15 mph, the average velocity of the trip is less than 20 mph
>>8203859
ninja'd
>>8203859
Yeah, I think that I got that far in my thinking, but I still don't think I quite understand it.
>The reason it's lower is because you spend less time traveling 25 mph, since it takes less time to cover the 5 miles.
Yes, but on the other hand, it takes more time travelling 15 mph, since it takes more time to cover the 5 miles.
>>8203870
> Since it takes longer to travel 5 miles at 15 mph, the average velocity of the trip is less than 20 mph
Yes, but it also is short travelling 5 miles at 25 mph
at 20mph the time it takes to travel 10 miles is 10/20 (0.5)
at 25 it's 10/25 or 2/5ths
at 15 it's 10/15 or 2/3rds
2/5 + 2/3 = 16/15
16/15 / 2 = 8/15 = 0.533
if you traveled at 39mph for 5 miles and 1mph for 5 miles the increased speed of the first half wouldn't make up for the 5 hours the second half takes
>>8203880
>if you traveled at 39mph for 5 miles and 1mph for 5 miles the increased speed of the first half wouldn't make up for the 5 hours the second half takes
Yes, but why?
>you should be looking at average speed over time
If you are driving for a longer time at a slower speed than at a higher speed, the average is skewed below 20mph. Average speed is all that matters in this calculation, so the car with a higher average speed will complete the trip faster.
>>8203883
because the original trip at 20mph was 1/2 hours, by decreasing the speed by 19 for half the distance you guarantee a trip of 5 miles at 1mph which will always be 5 hours, going at 39mph for the other half won't take back the extra time you've spent
>>8203879
>Yes, but it also is short travelling 5 miles at 25 mph
You travel for a longer period of time at 15 mph than at 25 mph, so the 15 mph part "weighs" more I guess. That pulls the average speed down, which increases the travel time.
If you traveled an equal amount of [math]time[/math], not distance, at 15 and 25 mph, then the travel time would be the same as when you would travel 20 mph the whole trip.
>>8203885
example: if you drive for 20 minutes at 10mph and 10 minutes at 20mph your average speed is not 15mph. It's more like 13 (rough estimate). The respective distances travelled aren't relevant.
>>8203829
Imagine if I travelled 10 miles really, really slowly, like 0.000000001 mph, then travelled 10 miles at 39.999999999 mph. The total is 40 mph (if I got the decimal places right), but obviously doing 10 miles at 0.0000000001 mph is going to take a loooooong time - much longer than half an hour.
That doesn't surprise you, does it
>>8203910
Not OP, but I don't think this is helpful. Why are you adding the speeds? Also looking at the distances travelled is what makes the question confusing in the first place
>>8203859
Well, thread won on first reply. It's the reason why going 45 mph on a dank country road gets you farther than 60 on a city road with red lights. The time wasted going 0 mph is impossible to make up.
Didn't mean to sound harsh, but OP already responded to a seemingly identical post here.
>>8203883
