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Now and Then

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2
We had some really good ideas sent in for the times that may be expected in the $2012$ games
There was a range of ideas as follows;

$100$ metres $9.50$ to $10.00$ secs
$200$ metres $18.56$ to $20.30$ secs
$400$ metres $38.52$ to $ 43.92$ secs
$800$ metres $99.00$ to $108.00$ secs
$1500$ metres $211.00$ to $224.00$ secs

So we will have to wait for the games to see if they are the correct figures! Most results came from Manorfield Primary School from these pupils: Natasha, Jennifer, Lauren, Isabelle, Emily, Ben, Heather, Becky, Olivia, Hannah, Kayla, Abbie-mai, Chloe, Jade, Stephanie and Nazra.

Joe from St. Joseph's School wrote;

It can not keep going on in the same pattern as the difference between the time and  the improved results, because if it did, it would go into negative results and races can't be run in minus numbers. See these results up until year 2828.
Patrick from Manorcroft Primary school, Egham wrote the following thorough explanation of what they did at his school.

1/ We first compare the rates and find how much they improved [a]. Then we divide [a] by the number of years ($40$) to find the $%/$year rate [b]. We × [b] by $64$ (the number of years later) to find the improvement rate [c],
∴ × [c] by the time (e.g. $400$m is $50$ secs → $46.2$ secs
∴ $46.2$ × improvement rate [c] = new time).
2/ But people can’t go on competing in the Olympics for $40$ years.
There are food changes, different exercise schedules & completely different people.
3/ ∴ I think there is no pattern to predict the results.

Well thank you all, it was a very worthwhile activity for you all to get involved in.