My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

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


Thanks Tree2Thanks
  • 1 Post By DarnItJimImAnEngineer
  • 1 Post By tahirimanov19
Reply
 
LinkBack Thread Tools Display Modes
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)}?
Ganesh Ujwal is offline  
 
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
DarnItJimImAnEngineer is offline  
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
tahirimanov19 is offline  
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?
skipjack is offline  
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 View Post
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.
tahirimanov19 is offline  
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.
DarnItJimImAnEngineer is offline  
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 .
idontknow is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
average, explain, problem, speed, step



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How to find average speed for this problem? Ganesh Ujwal Elementary Math 1 October 3rd, 2019 02:52 AM
average speed problem shunya Elementary Math 11 April 8th, 2016 04:08 PM
Could somebody explain this step? mathguy32190 Algebra 2 March 3rd, 2015 10:30 AM
Help with average speed problem please? RealMadrid Physics 0 September 10th, 2012 06:53 AM
Average speed problem haftakhan Algebra 1 August 11th, 2011 10:14 PM





Copyright © 2019 My Math Forum. All rights reserved.