Watching the TdF and currently there's a breakaway with 14min lead and 54km to go.
My question is;
Can you come up with a formula that say how much faster the peloton needs to go to catch them before the finish.
Before anyone says 'get a life' or some other BS, this is just for the challenge and to see if it can be done. Some of us find maths fun you know 😉
You work for edexcel and have run out of resit questions. Where do I claim my £5?
Already been done I'm afraid! http://www.cyclingnews.com/news/tour-de-france-what-are-the-chances-of-breakaway-success/
5km/h
Yes, I can.
1) work out how long the breakaway willl take to get to the finish as their current speed (distance / speed)
2) work out how fast the peleton need to go to get to the finish in that same amount of time (distance / time)
As the break away changes speed the peleton's required speed will also change.
I don't think you can unless you know what their average speed will be.
They need to save 15.6s/km - a 14 min lead is quite a considerable advantage. It's a hilly stage today, isn't it?
2) work out how fast the peleton need to go to get to the finish in that same amount of time (distance / time)
But you don't know how far they are away, you only have a gap time so your 'distance' in the equation is unknown.
The cyclingnews equation is a little more complicated than I expected, but then it does give more information than I asked for.
I wondered if it could be expressed as a percentage in terms of the dist to go and gap time. For example; they need to go '5% faster' than the leading group.
You can't do it as a percentage unless you know them in a consistent way, i.e. time gap and time to finish or distance gap and distance to finish.
If you know their current speed and the gap is steady, you can work out the distance gap.