Help Jeff
Math brain teasers require computations to solve.
Jeff likes racing his little sports car, but he knows that safety should always be kept in mind, so he practices regularly. On one particular day, Jeff goes out to the practice track and does two laps at an average of 100 km/h, two laps at an average of 102 km/h, two laps at an average of 140km/h and two laps at an average of 150 km/h. Now Jeff would like to know what his average speed was during that practice session. Can you help him?
Answer
The answer is 119 and NOT 123. How? Well, you have probably made the fatal assumption that time is not important here in Jeff's world and yet you should know that time is important everywhere.
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Comments
(user deleted)
Nov 21, 2001
 I may be thick but this makes no sence.
you say Keep in mind that each 2nd lap of track
takes less time than the previous two! but this is wrong the first lap could be the quickest of all (followed by the slowest) 
bobbrt
Jun 19, 2002
 The answer is correct. Here's the math: Assume that the track is 1km in length (the length really doesn't matter, but 1 km makes the math easy). The first lap takes (1 km)/(100 km/hr) = 0.01 hr = 36 seconds. The third lap takes (1 km)/(102 km/hr) = 0.0098 hr = 35.294 seconds. By the same math, lap 5 takes 25.714 seconds and lap 7 takes 24 seconds. To get the average speed you need to take the total time and divide by the total distance. Total time = (36 + 35.294 + 25.714 + 24) * 2 = 242.017 seconds. Total distance is 8 km. Therefore 8 / 242.017 = 0.033 km/sec = 119 km/hr. Hope that helps. 
scoutman
Oct 22, 2003
 Sorry, bobbrt, but the math goes like this: you are given an average speed per two laps. To find the average speed of a multiple of those two laps, you take the given average speed of each set of two laps, add them together, and divide by the multiple. Thus, given the numbers in this teaser, the average overall speed is 123. On a side note, I think the last line of the answer is refering to 199 Km/hr being faster than 123 Km/hr. Last time I checked, that's wrong. 
Bobbrt
Oct 23, 2003
 OK, scoutman, let's assume that you are right. Let's change the numbers a bit. Say he runs two, onekm laps: the first at 1 km per hour and the second at 1000 km per hour. You should agree that the entire trip takes just over 1 hour (1 hour for the first lap and a few seconds for the second lap). In that time he travels 2 km. According to you, his average sped is 500.5 km/hour. Why is it then, when averaging 500 km/hour it took him a whole hour to travel two measly km? The answer is that an average speed is found by taking the TOTAL distance and dividing by the TOTAL time. In this example, the average speed is just under two km per hour. It is because he spends much more time travelling 1 km/h than he does travelling 1000 km/h, giving the slow speed much more weight when calculating the average speed. If he travelled each speed for the same amount of TIME, then you could just average the numbers to get the overall average speed. The answer to this teaser is absolutely correct. 
Bobbrt
Oct 23, 2003
 ...although the explanation of the answer isn't very good. Oh, and regarding the secondtolast line of the answer, he is just saying that laps 3 & 4 are each faster than 1 & 2, 5 & 6 are each faster than 3 & 4, etc. 
Rowsdower
Jan 11, 2004
 Um, I agree with Bobbrt, not because I'm as good at math as he is, but because I know that racecars accelerate and their performance improves as their tires warm and so forth, and also because I'm in to NASCAR. Futhermore, the teaser explains this (in a sort of limited way), and before anyone argues with a teaser they need to be SURE they are right. 
Maslin
Jun 09, 2005
 Can I know in very simple terms why time matters in this case? Very simple terms 
Methlos
Mar 14, 2006
 whos jess? 
dishu
Jun 01, 2006
 Maslin I dont know what's your age so I dont know wheter you have studied the chapters on speed, distance and time.
But when you study, you will come to know that speed, distance and time are related concepts.They cannot be considered in solace.Also they are numeric relations and not just numbers so a simple average will not work.
Plus if you have gone out in a car, you will know that time taken is much less for the same distance when the car is driven fast, and much slow when car is driven slowly. 
DEJL
Aug 22, 2006
 Huh?Hard. 
Jimbo
Mar 25, 2007
 Difficult to understand the comments when a large chunk of the answer has been obviously edited out. I suppose if a teaser has no explanation accompanying the answer then it gives an opportunity for someone like Bobbrt to provide one within the comments. (His explanation is quite correct BTW). 
(user deleted)
Feb 09, 2008
 BORING!!!!!!!!!!!!!!!!!!!!!
that is how you spell BORING!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
sourdough
Jun 23, 2008
 My goodness! SourDough's a tad perplexed but liked this nevertheless!
$D 
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