# Swimming Problem Maths Investigation.

Extracts from this document...

Introduction

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## 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

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)

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.

This student written piece of work is one of many that can be found in our GCSE Comparing length of words in newspapers section.

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