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  • Level: GCSE
  • Subject: Maths
  • Word count: 2913

Swimming Problem Maths Investigation.

Extracts from this document...

Introduction

:

Swimming Problem Maths Investigation

Introduction

A group of swimmers are following a training schedule that requires them to dive into the water and swim one length of the swimming pool. They must keep doing this until they have completed 20 lengths. For safety’s sake they have been allocated a single lane of the pool and all the swimmers must swim in the same direction in single file.

Half of the swimmers say that it will be quickest always to swim in the same direction, climbing out of the pool at the end of each length to rejoin the queue. The other swimmers want to climb out of the pool at the end of each length, wait until all the simmers have completed the length and then swim back one by one in the opposite direction.

I have to pick the method that I prefer and I have chosen the one where they get out at the end of each length, wait until all the swimmers have completed the length and then swim back in the opposite direction. I have chose this way because then the swimmers don’t have

...read more.

Middle

I will now change the variables to see what happens to the results. I will keep the length of the pool at

25 metres but make it so the swimmers are swimming at a faster pace of 2ms. Here are the results.

Swimmer no

Length 1

2

3

4

5

6

7

8

9

10

1

12.5

70

127.5

185

242.5

300

357.5

415

472.5

530

2

17.5

75

132.5

190

247.5

305

362.5

420

477.5

535

3

22.5

80

137.5

195

252.5

310

367.5

425

482.5

540

4

27.5

85

142.5

200

257.5

315

372.5

430

487.5

545

5

32.5

90

147.5

205

262.5

320

377.5

435

492.5

550

6

37.5

95

152.5

210

267.5

325

382.5

440

497.5

555

7

42.5

100

157.5

215

272.5

330

387.5

445

502.5

560

8

47.5

105

162.5

220

277.5

335

392.5

450

507.5

565

9

52.5

110

167.5

225

282.5

340

397.5

455

512.5

570

10

57.5

115

172.5

230

287.5

345

402.5

460

517.5

575

I took 575 sec for 10 people to swim 10 lengths of a pool, which are 25 metres long and swimming at a constant rate of 2ms. This is a lot less time than when they were travelling a 1ms.

These is the results of the next 10 lengths

Swimmer No

Length 11

12

13

14

15

16

17

18

19

20

1

587.5

645

702.5

760

817.5

875

932.5

990

1047.5

1105

2

592.5

650

707.5

765

822.5

880

937.5

995

1052.5

1110

3

597.5

655

712.5

770

827.5

885

942.5

1000

1057.5

1115

4

602.5

660

717.5

775

832.5

890

947.5

1005

1062.5

1120

5

607.5

665

722.5

780

837.5

895

952.5

1010

1067.5

1125

6

612.5

670

727.5

785

842.5

900

957.5

1015

1072.5

1130

7

617.5

675

732.5

790

847.5

905

962.5

1020

1077.5

1135

8

622.5

680

737.5

795

852.5

910

967.5

1025

1082.5

1140

9

627.5

685

742.5

800

857.5

915

972.5

1030

1087.5

1145

10

632.5

690

747.5

805

862.5

920

977.5

1035

1092.5

1150

The total time it took for the swimmers to complete 20 lengths swimming at a constant speed of 2ms (metres per second) and starting swimming five seconds after the last person is – 1150 seconds which is 18 mins and 25 seconds.

Formula

I am now going to try and work out a formula in which to calculate the total time it takes to complete any amount of lengths at any speed and with any set distance between the swimmers.

The variables I am going to need for this formula are

T = Total time

L = Total time it takes for 1 swimmer to complete 1 length

A = Amount of lengths

N = Number of swimmers

G = Gap between two swimmers

D = distance of length

S = speed the swimmers are travelling

L = D/S                                                  

T = L + G*(N-1)

...read more.

Conclusion

If I had a lot more time and I was to change anything on this problem I would make the models more exact. I would find out actual swimming and walking times through testing and not just estimating. I would experiment on the average times it takes swimmers to swim 20 lengths. I would make the whole model more exact thus giving a more reliable result.

Based on the assumptions that I have made through this problem, the second method is the quickest way for the swimmers to complete 20 lengths. They walk using this method but they complete the 20 lengths in a lot less time than by using the other method.

...read more.

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