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Objective: 

To be able to form and solve equations

Algebra lesson

Job Requirements

Maths required:

•

Substituting into algebraic formulae

•

Solving equations

•

Solving simultaneous equations

Equipment required:

•

Pen

•

Calculator

Videos

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Introduction to the Coastguard

•

What challenges does the Coastguard face?

•

Why is Maths so important in Search and Rescue

activities?

Solving Equations - Saving Lives

•

Cruise ships have to carry lifeboats in case of

emergency.

•

Different lifeboats have different capacities.

•

Evacuating a ship needs to be carried out in a calm

manner. Overloading a life raft could have

extremely dangerous implications.

Lifeboat capacities

We can represent a ship’s lifeboat capacity with

simple notation, e.g. the P&O ‘Adonia’ has capacity

for 6L + 22D.

This means the ship has 6 large liferafts and 22 deck

liferafts and can hold (6x150) + (22x25) = 1450

persons.

Questions to consider?

1.

Why might a ship not want to reach its full

lifeboat capacity?

2.

How would you distribute lifeboats on a ship?

3.

Would it be better to fill a few lifeboats, or

spread people across lots?

Sample problems

1.

How many deck liferafts (D) would you need to hold

225 people?

2.

660 people are on a boat that needs to be

evacuated. There are 30 deck liferafts (D) on board.

To evenly distribute weight, how many should go on

each raft?

3.

821 people are on a boat that needs to be

evacuated. The boat has 3 standard liferafts (S) and 5

large liferafts (L). Once the standard liferafts have

been completely filled, how many should go in each

large liferaft to evenly distribute the weight?

Sample problems (solutions)

1. How many deck liferafts (D) would you need to

hold 225 people?

Let x = number of liferafts required

25x = 225

x = 225/25

x = 9

ANSWER: You would need 9 deck liferafts (D)

Sample problems (solutions)

2.

660 people are on a boat that needs to be

evacuated. There are 30 deck liferafts (D) on

board. To evenly distribute weight, how many

should go on each raft?

Let D = number of people on each liferaft

30D = 660

D = 660/30

D = 22 people

Sample problems (solutions)

3.

821 people are on a boat that needs to be

evacuated. The boat has 3 standard liferafts (S) and

5 large liferafts (L). Once the standard liferafts have

been completely filled, how many should go in

each large liferaft to evenly distribute the weight?

3S + 5L = 821

(S and L represent the number of people on liferafts)

(3x47) + 5L = 821 

(the 3 S lifeboats are filled with 47 people each)

141 + 5L = 821

5L = 680 

(821 - 141 = 680)

L = 136 people 

(680 divided by 5 boats = 136)

Challenge problem (sim. equations)

A cruise ship has 900 passengers on board. They

have two different lifeboats on board - Type A and

Type B. The passengers can fill the lifeboats

completely in the following ways:

6 type A boats and 15 type B boats

2 type A boats and 17 type B boats

How many people does each boat hold?

Challenge problem – solution