1. Objective: To be able to form and solve equations Algebra lesson SaRalgebra.lgfl.net

2. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Job Requirements Maths required: Substituting into algebraic formulae Solving equations Solving simultaneous equations Equipment required: Pen Calculator

3. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Videos Introduction to the Coastguard What challenges does the Coastguard face? Why is Maths so important in Search and Rescue activities?Why is Maths so important in Search and Rescue activities?

4. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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.

5. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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. Deck liferaft (D)25 persons Standard liferaft (S)47 persons Large liferaft (L)150 persons Marine Evacuation System (M) 370 persons

6. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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?

7. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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?

8. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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)

9. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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

10. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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)

11. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net 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?

12. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Challenge problem – solution