Quizzzzzzzzzz

Imagine driving to a destination to play poker.

The trafic is so heavy , you are able to average

only 40mph. However ,on your return trip you are able to breez along at an average speed of 60 mph

What would be your average speed for the whole journy?


THIS QUIZE IS FROM THE BOOK WHEN TO HOLD'EM AND WHEN TO FOLD'EM

I will drive 40 mph for a longer time than I drive 60 mph, so the average will be less than 50. Say the distance is 120 miles each way. Then it will take 3 hours one way and 2 hours the other way for a total of 5 hours to drive 240 miles which would be an average speed of 48 mph. This will be the average speed regardless of the distance.

..........

48 miles per hour.


Bob T.

For any electrical engineers in the crowd, if we derive a formula for averaging speeds, it would look alot like the formula for calculating parallel resistance.


Say the total distance each way is d, and the speeds are s1 and s2 for times t1 and t2. Then:


avg speed = 2d/(t1+t2)


= 2d/(d/v1 + d/v2) = 2/(1/v1 + 1/v2)


= 2v1v2/(v1+v2)


Same as parallel resistance except for the 2.

Basically you calculated the Harmonic mean of the two speeds. Does the geometric mean have any significance when applied to speeds?


averge(a,b) = (a+b)/2 = mean or average


1/average(1/a, 1/b) = 2 a b /(a + b) = harmonic mean


exp(average(log(a), log(b))) = sqrt(a b) = geometric mean.