Lancashire
Mathematics Challenge
2009
District finals
Around the World in 80 days
LMC
2009
LMC
2009
Switzerland
LMC
2009
Swiss Railway
Switzerland is a very mountainous
country and the railways are designed
to cope with this terrain. Different
systems are used to cope with
different gradients.
u
up
LMC
2009
a across
The distance
up u divided
by the distance
across a is
called the
GRADIENT of
the slope.
Swiss Railway
The 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.
LMC
2009
The steepest funicular railway has a gradient of 0.89
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
LMC
2009
If cars are joined together in a train the
maximum gradient it can run on is 0.125
Swiss Railway
Phil 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.
LMC
Write down which type of railway would be
2009 suitable for each one.
Audience Quiz
Type of
railway
Maximum
gradient
LMC
2009
Ordinary Funicular Rack and Rack and
engine
pinion
pinion
(single)
(train)
0.09
0.89
0.5
0.125
Egypt
LMC
2009
Ancient Egyptian Number System
LMC
2009
South Africa
LMC
2009
Diamond Mining in South Africa
LMC
2009
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
LMC
2009
2
3
4
Australia
LMC
2009
Sheep Farming in Australia
LMC
2009
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?
LMC
2009
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
LMC
2009
Making Coffee in Brazil
• 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
LMC coffee.
2009
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?
LMC
2009
• Americano coffee?
• Brazilian coffee?
LMC
2009
Chorley
LMC
2009
Phil Arrives Home
Exchange rates:
LMC
2009
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
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.
LMC
2009
Winning in which country would give him the
most money when he exchanged it for pounds
sterling?
Lancashire
Mathematics Challenge
2009
District finals
Around the World in 80 days
LMC
2009