Runners

Math Trivia: There are 12 runners running. How many different ways can they be 1st, 2nd, and 3rd place?

admin — Wed, 16 May 2012 22:06:22 +0000

There are 12 runners running. How many different ways can they be 1st, 2nd, and 3rd place?

(its either a two digit number or three)

I suspect that the answer that you want is 220 but I disagree with it.

12 x 11 x 10 = 1320
The first can be any of 12
The second can be any of 11 (one already 1st)
The third can be any of 10 (2 already 1st and 2nd)

Therefore there are 12 x 11 x 10 permutations of this result = 1320.
This answer above is the answer I would normally have given. It is the equivalent of12P3 and equals 12!/9!.

HOWEVER as you see the answer has 4 digits and so I suspect that you want combinations rather than permutations. 12C3 = 12! /9!3! = 1320/6 = 220
This is the answer that you presumably want

It must be stated though that if you want combinations then you regard A finishing firrst B finishing 2nd and C finishing third as EXACTLY the same as C finishing first A finishing second and B finishing third or any of the other arrangements that you can make of these 3.
Three people can be arranged in 3! or 6 different ways
ABC, ACB, BAC, BCA, CAB, CBA
therefore for every combination of 3 people you can get 6 permutations. Therefore that is why the 1320 permutations is divided by 6 = 220 combinations.

IN conclusion – the answer that you probably want is 220 COMBINATIONS but I don’t like it. I would have thought 1320 PERMUTATIONS is betrter in this case because there IS a difference between first second and third places.

Two runners start running from the same point at the same time.?

admin — Tue, 08 May 2012 18:20:29 +0000

2.Two runners start running from the same point at the same time. The first runner runs north at 3 miles per hour, and the second runner runs southeast at 4 miles per hour.

B)The runners are each carrying walkie-talkies with a signal range of 20 miles. At what time do the runners lose contact with each other?

Hello

Let O be the origin point of the two runners;
let A be the first runner;
let B be the second runner;
let α be the measure of the angle BÔD.

By definition of the problem:
OA = 3t is the distance made by the first runner.
OB = 4t is the distance made by the second runner.
α = 3π/4

The law of cosines state:
AB² = OA² + OB² – 2.OA.OB.cos(α)
AB² = (3t)² + (4t)² – 2.3t.4t.cos(3π/4)
AB² = 25t² – 24t².(-√2/2)
AB² = 25t² – 24t².(-√2/2)
AB² = t²(25 + 12√2)
AB = t.√(25 + 12√2)

So if AB, the distance between both runners, is 20 miles, elapsed time is:
t = AB / √(25 + 12√2) = 20 / √(25 + 12√2) ≈ 3,09 hours.

So the runners will lose contact approximatively 3 hours and 5 minutes after leaving each other.

The answer of antoine2546, that 10 hours, is both wrong and unrealistic since, in 10 hours, both runners would have run respectively 30 and 40 miles, way over the signal range of 20 miles!

Logically,
Dragon.Jade

Is it possible to attach carpet runners over steps that are carpeted?

admin — Wed, 08 Feb 2012 04:42:39 +0000

I have light grey carpets on my steps that get very dirty. Without tearing the old carper up can i have a carpet runner (not plastic) placed over the steps that are secure? No carpet runners are meant to be … Continue reading →

Can 1 step fuel cleaner damage my car if the tank is nearly empty when it is added?

admin — Fri, 03 Feb 2012 06:04:07 +0000

One step was added to my 2005 Toyota 4 Runner when the tank was nearly empty. I drove about 3 blocks and filled the tank. My fuel mileage immediately dropped from 20-22 mpg to about 14 and has stayed 14 to 16 mpg since thru several tanks of gas. The only other things that were done to my car at that same time was a oil change and the battery terminals were cleaned. Can the fuel cleaner have damaged something causing this drop in fuel mileage?

You fouled/damaged the front oxygen sensor (likely). Never on an empty tank.

a runner with a mass of 52 kg has a momentum of 218 kg x m/s. What is the runners velocity?

admin — Sun, 29 Jan 2012 07:41:54 +0000

momentum = mass x velocity

velocity = momentum/mass = 218kgm/s / 52 kg = 4.2 m/s

how do you stop a runner rug from curling on ends ?

admin — Fri, 27 Jan 2012 00:56:34 +0000

home depot or lowes sell a product just for this. you put it underneath each corner of the rug and it stops the curling and prevents people from tripping.

Who are some great underdog track runners who have left their footprint in track?

admin — Tue, 24 Jan 2012 10:03:14 +0000

Hi, I’m trying to inspire my middle school track kids (there just starting out) and I wanted to give them some examples of great track runners who didn’t start out so great at first, but with hard work and determination have succeeded. Thank You!

Louis zamperini. Hope I spelled that right.
He had a really troubled childhood but channeled it all into running and broke the record for the fastest lap while running the Olympic mile

Can I install a stair runner with tack nails alone?

admin — Tue, 17 Jan 2012 04:22:34 +0000

If not, what more do I need?

Also, how long should I wait to install the runner after painting the stairs?

Personal experience, anecdotes, etc. will be most helpful.

Thanks in advance!

http://www.howtodothings.com/video/installing-a-stair-runner

What do i need if i want to put a 70′s kit on my Gilera Runner?

admin — Tue, 10 Jan 2012 02:48:58 +0000

I want to put a 70cc kit on my Gilera Runner.
Firstly any recommended kits that are better?
What carb/jet sizes will i need?
Any advice would be appreciated
Thanks

Firstly make sure any 70cc kit you get will fit a Piaggio type engine. If you get a high-end 70cc kit you will need a bigger carb, 17,5 would do fine. For the jet size, i would say for a start, get one around 95 or so, smaller chance of overheating or destroying your engine if your running rich. If 95 is too big, move down 5 sizes and try again. If it feels too lean(engine revs to max in just 1/2 turn of the throttle) get a bigger jet. There are a lot of scooter-tuning forums where you could ask, people there are very friendly.

How do you get to the battery on a Gilera Runner FX 125?

admin — Thu, 05 Jan 2012 03:25:17 +0000

I have had a 180 SP, before and batter was under the seat. I am just having trouble locating the batter on the FX model I bought yesterday. What do I need to take off to get to the battery? … Continue reading →