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18 Mar 2005, 15:14
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Laticia can run three and a half 6 minute miles before she gets tired and has to slow down to a pace of 8 minutes per mile. Johanna, her competitor on the track team, always runs 7-minute miles, and can keep running at this speed for hours. Which of the following races is the longest that Laticia can run without Johanna running it in less time?
3.5 miles
4.5 miles
6 miles
7 miles
8.5 miles
3.5 miles
4.5 miles
6 miles
7 miles
8.5 miles
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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18 Mar 2005, 16:11
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cloaked_vessel
7 miles.
Here's my approach.
L runs 3.5 6-min miles in 21 mins. In 21 mins, J has run @ 7min/mile, 3 miles.
Thus when L slows down, J is 0.5 miles behind her.
If J catches up with L in t minutes (from now on),
t/8 + 1/2 = t/7
7t + 28 = 8t
t = 28 mins.
In 28 mins, L runs an additional 3.5 miles. J runs 4 miles.
Total distance run by both is 7 miles.
Please let me know if someone can hit the answer by some other approach.
18 Mar 2005, 20:16
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You can also approach this problem by:
3.5 * 6 + 8(x-3.5) < 7x
x<7
3.5 * 6 + 8(x-3.5) < 7x
x<7
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
