lmc 2009 lancashire mathematics challenge 2009 district finals around the world in 80 days

LMC2009

Lancashire Lancashire Mathematics ChallengeMathematics Challenge

20092009

District finalsDistrict finals

Around the World in 80 days

LMC2009

Switzerland

LMC2009

LMC2009

Swiss RailwaySwitzerland is a very mountainous

country and the railways are designed to cope with this terrain. Different

systems are used to cope with different gradients.

uup

a across

The distance up u divided by the distance across a is called the GRADIENT of the slope.

LMC2009

Swiss RailwayThe steepest gradient an ordinary train can cope with is 0.09

In a funicular

railway the car is fixed to a cable which pulls it up the hill.

The steepest funicular railway has a gradient of 0.89

LMC2009

Swiss Railway

Mountain railways use a rack and pinion system. A toothed wheel runs along a toothed rail.

If a single car uses this method the gradient can go up to 0.5

If cars are joined together in a train the maximum gradient it can run on is 0.125

LMC2009

Swiss RailwayPhil needs your help!

He has dropped the pictures of the railway bridges and cannot remember which is which! It would help if he knew which type of railway used each bridge.

You have the pictures. Find the gradient of each railway, correct to two decimal places.

Write down which type of railway would be suitable for each one.

LMC2009

Audience QuizType of railway

Ordinary engine

Funicular Rack and pinion (single)

Rack and pinion (train)

Maximum gradient 0.09 0.89 0.5 0.125

Basle line

Max gradient 7%

Zurich passMax gradient ¼

Geneva tunnel

Max gradient ¾

Lucerne inclineMax gradient 57%

Egypt

LMC2009

LMC2009

Ancient Egyptian Number System

South Africa

LMC2009

LMC2009

Diamond Mining in South Africa

LMC2009

Audience Quiz

This shape is often called a diamond but what is its mathematical name? This is your clue for number 5 in your crossword.

Here are the other clues:

1 2

3 4

Australia

LMC2009

LMC2009

Sheep Farming in Australia

LMC2009

Audience Quiz

Ralph the ram has 20 ewes. When they lambed, ¾ of the ewes had twins and the rest had triplets. How many lambs did Ralph’s ewes have?

Eunice, one of Ralph’s ewes, gave birth to triplets. The lambs weighed 5.5 pounds, 6 pounds and 7.2 pounds. What was the average weight of the lambs to the nearest tenth of a pound?

Brazil

LMC2009

LMC2009

• To make Espresso coffee he needs to use 3 cups of water with 2 spoons of ground coffee.

• To make Americano coffee he needs 5 cups of water for each 3 spoons of ground coffee.

• For Brazilian coffee he needs 4 cups of water for every 3 spoons of ground coffee.

Making Coffee in Brazil

LMC2009

Audience Quiz

Espresso: 3 cups water to 2 spoons coffee

Americano: 5 cups water to 3 spoons coffee

Brazilian: 4 cups water to 3 spoons coffee

Phil gets the water in containers which hold 30 cups water. How many spoons of coffee should he add to each container to make:

• Espresso coffee?

• Americano coffee?

• Brazilian coffee?

LMC2009

Chorley

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LMC2009

Phil Arrives Home

Exchange rates:Exchange rates:

Switzerland 1 Swiss Franc = 60p

Egypt 1 EGP = £0.1261

South Africa £1 = 14.55 ZAR

Australia 1 AUD = £0.448

Brazil £1 = 3.33 BRL

LMC2009

Audience Quiz

1 SF = 60p

1 EGP = £0.1261

£1 = 14.55 ZAR

1 AUD = £0.448

£1 = 3.33 BRL

While in each country Phil bought a lottery ticket hoping to win 1 million of each country’s currency.

Winning in which country would give him the most money when he exchanged it for pounds sterling?

LMC2009

Lancashire Lancashire Mathematics ChallengeMathematics Challenge

20092009

District finalsDistrict finals

Around the World in 80 days