My Math Forum Explain this step in Average speed problem?

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 October 3rd, 2019, 10:21 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 477 Thanks: 1 Explain this step in Average speed problem? What is the average speed of a man who works at 1kmph for 1 hour, 2 kmph for 2 hours........ till 10 kmph for 10 hours? A) Average speed = (Total distance)/(Total time) = (1*1+2*2+3*3…….10*10)/(1+2+3****+10) = {1/6 n(n+1)(2n+1)}/ {1/2 n(n+1)} = 2n+1/3; (n = 10) = 7 Explain this step in Average speed problem: {1/6 n(n+1)(2n+1)}/ {1/2 n(n+1)}?
 October 3rd, 2019, 10:51 PM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 Those are tricks for quickly finding the sums 1²+2²+3²+...+n² and 1+2+3+...+n. The second one, you can visualise as making a "triangle" of a row of 1 block, a row of 2 blocks, a row of 3 blocks, a row of 4 blocks, etc. If you make a second triangle, turn it around, and put it next to the first, you get a rectangle that is n blocks by n+1 blocks. (There was also a possibly apocryphal story about some maths or physics genius doing this when his teacher tried to give him busy work to shut him up.) The first one is similar, but instead of a triangle, you're building a pyramid with a plane of 1x1 block, a plane of 2x2 blocks, a plane of 3x3 blocks, a plane of 4x4 blocks, etc. Thanks from topsquark
 October 4th, 2019, 02:58 AM #3 Senior Member   Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 132 Thanks: 49 Math Focus: Area of Circle It is a weighted average $\dfrac{w_1a_1+w_2a_2+...w_na_n}{w_1+w_2+...w_n}$, sort of (in this case, what I call quadratic average $\dfrac{{a_1}^2+...{a_n}^2}{a_1+...a_n}$). $Total Distance =Distace_1 + Distance_2 + ... Distance_{10} = 1^2+2^2+...10^2=\dfrac{10 \times 11 \times 21}{6}=385$ $Total Time = Time_1+Time_2+...Time_{10}=1+2+...10=55$ $Average Speed=\dfrac{TotalDistance}{TotalTime}=385/55=7$ Thanks from idontknow
 October 4th, 2019, 03:54 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,035 Thanks: 2271 Any guesses as to what kind of work the man is doing?
October 4th, 2019, 04:31 AM   #5
Senior Member

Joined: Mar 2015
From: Universe 2.71828i3.14159

Posts: 132
Thanks: 49

Math Focus: Area of Circle
Quote:
 Originally Posted by skipjack Any guesses as to what kind of work the man is doing?
Self-indulging, while slow driving... Or fast walking...

Last edited by skipjack; October 4th, 2019 at 03:03 PM.

 October 4th, 2019, 07:29 AM #6 Senior Member   Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 For 55 hours? Now that's what I call stamina.
 October 4th, 2019, 08:35 AM #7 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 The universe is light and full of stamina .

 Tags average, explain, problem, speed, step

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Ganesh Ujwal Elementary Math 1 October 3rd, 2019 02:52 AM shunya Elementary Math 11 April 8th, 2016 04:08 PM mathguy32190 Algebra 2 March 3rd, 2015 10:30 AM RealMadrid Physics 0 September 10th, 2012 06:53 AM haftakhan Algebra 1 August 11th, 2011 10:14 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top