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March 8th, 2017, 02:31 AM   #1
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Arrow Unknown Race Times

(Can you please explain clearly how you found the solution to this question as I'm only a Year 7)

In a 5000m race, the winner finishes 200 metres ahead of second and 600 metres ahead of third. Assuming the runners run at a constant speed, to the nearest integer how many metres ahead of third will second finish?

I tried using
time=distance/speed

formula and I replaced it with the distances between them and pro-numerals for the speed, but then I got stuck. I found out the answer in the internet to be 417 m but I didn't understand how they got the answer because it was in Year 9 format. Can anyone help me?
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March 8th, 2017, 05:08 AM   #2
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Math Focus: Calculus/ODEs
At the time the winner crosses the finish line, the second place runner has run 4800 m. Since the runners have constant speeds, the distances between them is increasing linearly so we may state:

$\displaystyle \frac{400}{4800}=\frac{d}{5000}$

Simplify

$\displaystyle \frac{1}{12}=\frac{d}{5000}$

Thus:

$\displaystyle d=\frac{5000}{12}=\frac{1250}{3}\approx417$
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