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I have a simple word problem involving division of fractions:

Dan and Bart are competing in a 100-meter sprint. Dan can run 22/7 metres a second, and Bart can run 41/2 metres in 56/9 seconds. Which contestant finishes first, and by how many meters ahead of the other?

If anyone can help me understand the process of solving this? I'm currently studying for the GED, and I'm having trouble trying to find a solution. I've tried converting the fractions to decimals to help me understand better. So, Dan runs 3.14 metres per second and Bart runs 20.5 metres per 6.22 seconds.

After this I tried multiplying Dan's metres per second by 6.22, so he would be running at 19.53 metres per 6.22 seconds? Now I divide 100 metres by their metres and multiplying by seconds.

Dan = 5.12 x 6.22 = 31.84 seconds per 100 metres

Bart = 4.87 x 6.22 = 30.29 seconds per 100 metres

Now I find myself stuck trying to answer by how many meters ahead of the other. If anyone could show their process of solving it, would be greatly appreciated! Thank you so much!

linada
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    Hint: how many meters would Dan have run in 30.29 seconds (when Bart crosses the finish line)? – lioness99a Feb 17 '20 at 11:44
  • Hi, thank you for the hint! So here is what I just tried. I divided Bart's time (30.29) by Dan's time (31.84) to get 0.95 and multiplied that product by 100 metres to get 95. Meaning Bart would beat Dan by 5 metres in the 100 metre sprint? – linada Feb 17 '20 at 11:58
  • Sounds good to me – lioness99a Feb 17 '20 at 12:00
  • Thank you again! Would rep you if I knew how. – linada Feb 17 '20 at 12:07
  • You can only give rep to answers, and the hint I gave wasn't worth putting in an answer as it didn't fully answer the question – lioness99a Feb 17 '20 at 12:27

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Dan = 5.12 x 6.22 = 31.84 seconds per 100 metres

Bart = 4.87 x 6.22 = 30.29 seconds per 100 metres

Bart wins the race. Dan is .95x slower than Bart and loses the sprint by 5 metres

linada
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