A question of C7 speed
10-10-2018, 11:29 PM
#41
Race Director
Member Since: Mar 2001
Location: Bonneville Salt Flats, 223mph Aug. '04
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Who CARES? Just STEP on it!!! 
10-11-2018, 11:58 AM
#42
Burning Brakes
Thread Starter
Well done, class. Several of you nailed it -- or were on the right track.
60 miles per hour = 1 mile per minute; to average 60 mph over 2 miles is to cover that distance in 2 mins.
30 miles per hour = 0.5 miles per minute = 1 mile per 2 mins.
The first mile at 30 mph takes 2 mins, so even if you were to travel the second mile at the speed of light, you would still average less than 60 mph over the two miles. It's not possible to cover the first mile at 30 mph and average 60 mph over the two miles.
The answer is wonderfully counterintuitive. In 1934, Max Wertheimer sent Albert Einstein a letter in which he posed this problem. And even Einstein didn't "get it" until he started doing the calculations.
I've asked the moderators to send those of you who got it right a bottle of Louis XIII cognac. Enjoy!
60 miles per hour = 1 mile per minute; to average 60 mph over 2 miles is to cover that distance in 2 mins.
30 miles per hour = 0.5 miles per minute = 1 mile per 2 mins.
The first mile at 30 mph takes 2 mins, so even if you were to travel the second mile at the speed of light, you would still average less than 60 mph over the two miles. It's not possible to cover the first mile at 30 mph and average 60 mph over the two miles.
The answer is wonderfully counterintuitive. In 1934, Max Wertheimer sent Albert Einstein a letter in which he posed this problem. And even Einstein didn't "get it" until he started doing the calculations.
I've asked the moderators to send those of you who got it right a bottle of Louis XIII cognac. Enjoy!
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green2000 (10-11-2018)
10-11-2018, 12:06 PM
#43
Safety Car
10-11-2018, 12:14 PM
#45
Race Director
Well done, class. Several of you nailed it -- or were on the right track.
60 miles per hour = 1 mile per minute; to average 60 mph over 2 miles is to cover that distance in 2 mins.
30 miles per hour = 0.5 miles per minute = 1 mile per 2 mins.
The first mile at 30 mph takes 2 mins, so even if you were to travel the second mile at the speed of light, you would still average less than 60 mph over the two miles. It's not possible to cover the first mile at 30 mph and average 60 mph over the two miles.
The answer is wonderfully counterintuitive. In 1934, Max Wertheimer sent Albert Einstein a letter in which he posed this problem. And even Einstein didn't "get it" until he started doing the calculations.
I've asked the moderators to send those of you who got it right a bottle of Louis XIII cognac. Enjoy!
60 miles per hour = 1 mile per minute; to average 60 mph over 2 miles is to cover that distance in 2 mins.
30 miles per hour = 0.5 miles per minute = 1 mile per 2 mins.
The first mile at 30 mph takes 2 mins, so even if you were to travel the second mile at the speed of light, you would still average less than 60 mph over the two miles. It's not possible to cover the first mile at 30 mph and average 60 mph over the two miles.
The answer is wonderfully counterintuitive. In 1934, Max Wertheimer sent Albert Einstein a letter in which he posed this problem. And even Einstein didn't "get it" until he started doing the calculations.
I've asked the moderators to send those of you who got it right a bottle of Louis XIII cognac. Enjoy!
if I make a 50 on one test and want to have an average of 70 after the second I need to score a 90 on the second test.
Maybe you meant to include a time constraint in the original problem?
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Jmhornz71 (10-11-2018)
10-11-2018, 01:13 PM
#47
Drifting
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defaria (10-11-2018)
10-11-2018, 01:25 PM
#49
Safety Car
I still don't see why your average speed isn't 60 if you do one mile at 30 and another at 90. There was no discussion of completing two miles in two minutes in the OP.
if I make a 50 on one test and want to have an average of 70 after the second I need to score a 90 on the second test.
Maybe you meant to include a time constraint in the original problem?
10-11-2018, 02:55 PM
#51
Instructor
It's another lovely day driving your C7. Ahead of you is a hill. It's one mile up the hill, and one mile down the other side. If you average 30 mph going up the hill (one mile), how fast would you have to drive down the other side in order to average 60 mph over the entire two miles?
10-11-2018, 03:45 PM
#52
Race Director
Speed is not the same thing as a score on a test. A score is only one number, indeterminate of everything else. Speed is a ratio of distance and time. And we can see this in the term 60 MPH. The H is hour or time. But there is also distance. Both time and distance combine to formulate the speed or rate of travel. The only way you can average 60 MPH given the constraint of a distance of only 2 miles is to take 2 minutes to do it. So if you've used up your 2 minutes in the first mile going 30 MPH there is no way you can travel the second mile instantaneously in order to achieve an average speed of 60 MPH. Even the speed of light, which is the fastest possible speed, takes some amount of time to travel a mile. If you could instantaneously go from 30 MPH to light speed you'd be very close but not exactly achieve a 60 MPH average speed.
You guys arguing this reminds me of an old Steven Wright standup routine:
"I was driving on the highway and a cop pulled me over - he said did you know you were speeding, doing 85 miles per hour in a 60 mile per hour zone? I replied: yeah, but I wasn't planning on being out that long..."
I guess this site explains the argument you guys are making, which again seems focused on the outcome (how far) rather than the instantaneous rate of travel.
https://sciencing.com/calculate-aver...h-6954798.html
Last edited by pdiddy972; 10-11-2018 at 03:50 PM.
10-11-2018, 04:19 PM
#53
Instructor
distance is given - 1 mile up hill and 1 mile down hill
speed = distance/time
30 mph = 1 mile/120 seconds
90 mph = 1 mile/40 seconds
2 miles(distance) / 160 seconds(time) = 45mph
Math is NOT that hard
speed = distance/time
30 mph = 1 mile/120 seconds
90 mph = 1 mile/40 seconds
2 miles(distance) / 160 seconds(time) = 45mph
Math is NOT that hard
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defaria (10-11-2018)
10-11-2018, 04:20 PM
#54
Safety Car
You can disagree all you want, physics doesn't care.
The MPH speed of the car is simply a rate. It doesn't in any way imply time except when measuring distances travelled over time.
The question, as posed, doesn't suggest anything about the time in which the trip takes place.
Yes, you'll end up taking longer than 2 minutes and, as a function a full hour's trip, you'd be right that your average speed wasn't 60, but your average rate of travel was. And that's what the problem was asking. 30 + 90 = 120 / 2 = 60 average
Physics says your wrong, math says your wrong, the link you posted says your wrong, Einstein says your wrong but you insist that you disagree with all of that. Amazing...
But don't trust me. Present a scenario that you can travel 2 miles in more than 2 minutes and your average speed is considered 60 MPH.
I think what you are thinking is that you are trying to average two individual points of instantaneous speed, one being 30 MPH and the other being 90 MPH and then your averaging just those two individual instantaneous speed samples. But in reality there's an infinite number of samples of instantaneous speed that need to be accounted for that you are neglecting. That's not how it work. Average speed is the ratio of the distance traveled divided by the time it took to get there.
Last edited by defaria; 10-11-2018 at 04:21 PM.
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rasacrystal08 (10-11-2018)
10-11-2018, 04:30 PM
#55
Melting Slicks
Incorrect my friend. Dr. Brown's DeLorean can travel through time, so the speed of light is not a limiting factor. In fact, via time travel you could cover the distance in less time than the 1 mile in 2 minutes took, essentially making up time an average speed.
10-11-2018, 05:16 PM
#56
Race Director
You can disagree all you want, physics doesn't care.
The very phrase MPH does not imply but rather directly states the rate in terms of miles (M) per hour (H) or M/H. How can you say "It doesn't in any way imply time except when measuring distances travelled[sic] over time"?
The question sure does mention time as in the "H" in MPH. Even if we said "the car is traveling at an instantaneous speed of 60 MPH" we are effectively saying that at this current velocity, if we let an hour of time pass the car would be 60 miles from this point.
Your average rate of travel is your average speed and is defined (http://www.math.com/school/subject1/.../S1U2L3DP.html) as " rate equals distance divided by time: r = d/t" where r = the rate and d = distance (or in our case of MPH, the M) and t = time (or in our case the H in MPH). That's how it's defined. If you take more or less than 2 minutes to travel 2 miles your average speed is most definitely not 60 MPH. You've admitted that if you take longer than 2 minutes then "you'd be right that your average speed wasn't 60 (MPH <- implied)". But then you try to define this other thing that you're calling "average rate of travel", which is your average speed. You even say "The MPH speed of the car is simply a rate"!
Physics says your wrong, math says your wrong, the link you posted says your wrong, Einstein says your wrong but you insist that you disagree with all of that. Amazing...
But don't trust me. Present a scenario that you can travel 2 miles in more than 2 minutes and your average speed is considered 60 MPH.
I think what you are thinking is that you are trying to average two individual points of instantaneous speed, one being 30 MPH and the other being 90 MPH and then your averaging just those two individual instantaneous speed samples. But in reality there's an infinite number of samples of instantaneous speed that need to be accounted for that you are neglecting. That's not how it work. Average speed is the ratio of the distance traveled divided by the time it took to get there.
The very phrase MPH does not imply but rather directly states the rate in terms of miles (M) per hour (H) or M/H. How can you say "It doesn't in any way imply time except when measuring distances travelled[sic] over time"?
The question sure does mention time as in the "H" in MPH. Even if we said "the car is traveling at an instantaneous speed of 60 MPH" we are effectively saying that at this current velocity, if we let an hour of time pass the car would be 60 miles from this point.
Your average rate of travel is your average speed and is defined (http://www.math.com/school/subject1/.../S1U2L3DP.html) as " rate equals distance divided by time: r = d/t" where r = the rate and d = distance (or in our case of MPH, the M) and t = time (or in our case the H in MPH). That's how it's defined. If you take more or less than 2 minutes to travel 2 miles your average speed is most definitely not 60 MPH. You've admitted that if you take longer than 2 minutes then "you'd be right that your average speed wasn't 60 (MPH <- implied)". But then you try to define this other thing that you're calling "average rate of travel", which is your average speed. You even say "The MPH speed of the car is simply a rate"!
Physics says your wrong, math says your wrong, the link you posted says your wrong, Einstein says your wrong but you insist that you disagree with all of that. Amazing...
But don't trust me. Present a scenario that you can travel 2 miles in more than 2 minutes and your average speed is considered 60 MPH.
I think what you are thinking is that you are trying to average two individual points of instantaneous speed, one being 30 MPH and the other being 90 MPH and then your averaging just those two individual instantaneous speed samples. But in reality there's an infinite number of samples of instantaneous speed that need to be accounted for that you are neglecting. That's not how it work. Average speed is the ratio of the distance traveled divided by the time it took to get there.
Velocity and acceleration are likewise often conflated because acceleration is a rate of change of velocity (which itself has as a component, speed). My point is that if the question wants an average instantaneous velocity of travel of 60 the answer is 90. For those intent on extrapolating the distance traveled and working backwards to an effective MPH based on distance traveled there's obviously no answer since the 2 minutes was already spent in the first mile. Hence my answer since it's the only one that doesn't fall for the joke.
10-11-2018, 07:26 PM
#57
Safety Car
I don't know what you mean by "average instantaneous velocity of travel" but perhaps this sheds some light... https://www.enotes.com/homework-help...average-394370
10-12-2018, 07:44 AM
#58
Instructor
Well it's obviously a trick question because of this exact argument over distinction, similar to the falling tree in a forest with no one around revolves around debate of whether sound is a vibration of a medium (not requiring a listener) or whether sound is a perceptual concept only occurring in a mind (requiring a listener).
Velocity and acceleration are likewise often conflated because acceleration is a rate of change of velocity (which itself has as a component, speed). My point is that if the question wants an average instantaneous velocity of travel of 60 the answer is 90. For those intent on extrapolating the distance traveled and working backwards to an effective MPH based on distance traveled there's obviously no answer since the 2 minutes was already spent in the first mile. Hence my answer since it's the only one that doesn't fall for the joke.
10-12-2018, 08:13 AM
#59
I still disagree. The MPH speed of the car is simply a rate. It doesn't in any way imply time except when measuring distances travelled over time. The question, as posed, doesn't suggest anything about the time in which the trip takes place. Yes, you'll end up taking longer than 2 minutes and, as a function a full hour's trip, you'd be right that your average speed wasn't 60, but your average rate of travel was. And that's what the problem was asking. 30 + 90 = 120 / 2 = 60 average
You guys arguing this reminds me of an old Steven Wright standup routine:
"I was driving on the highway and a cop pulled me over - he said did you know you were speeding, doing 85 miles per hour in a 60 mile per hour zone? I replied: yeah, but I wasn't planning on being out that long..."
I guess this site explains the argument you guys are making, which again seems focused on the outcome (how far) rather than the instantaneous rate of travel.
https://sciencing.com/calculate-aver...h-6954798.html
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defaria (10-12-2018),
rasacrystal08 (10-12-2018)
10-12-2018, 08:20 AM
#60
Race Director
If I drive a mile at 30 MPH what was my average speed during that mile? 30
if I drive another mile at 90 MPH what was my average speed during that mile? 90
What was my average speed across both miles? 90 + 30 = 120. 120 / 2 = 60
if I drive another mile at 90 MPH what was my average speed during that mile? 90
What was my average speed across both miles? 90 + 30 = 120. 120 / 2 = 60