March 8th, 2017, 02:31 AM  #1 
Newbie Joined: Mar 2017 From: Australia Posts: 2 Thanks: 0  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 pronumerals 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? 
March 8th, 2017, 05:08 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 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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algebra precalculus, race, times, unknown 
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