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# Laticia can run three and a half 6 minute miles before she

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Laticia can run three and a half 6 minute miles before she [#permalink]  18 Mar 2005, 14:14
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
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Joined: 15 Mar 2005
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Re: running [#permalink]  18 Mar 2005, 15:11
cloaked_vessel wrote:
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

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.
_________________

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Manager
Joined: 13 Oct 2004
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You can also approach this problem by:
3.5 * 6 + 8(x-3.5) < 7x
x<7
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