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

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Director
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New post 03 Dec 2004, 19:52
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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?

A. 3.5 miles
B. 4.5 miles
C. 6 miles
D. 7 miles
E. 8.5 miles

Pls explain your answers.
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New post 03 Dec 2004, 20:54
D.
They both would run a distance of 7 miles in 49 mins.
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New post 04 Dec 2004, 01:21
D, both can run together till 8.03 miles.

if x is the distance they run in same time then,
(3.5/6) + (x-3.5)/8 = x/7
x=8.03, which means they can run 8.03 miles in same time.
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New post 04 Dec 2004, 16:19
For L :
Time T = 6.3,5+8.X where X is the distance over the 1st 3.5 miles

For J
T' = 7.3,5+7X

We have to consider T=T' id est 21+8X=24,5+7X : X=3,5

J and L will need the same time to run the 1st 7 miles of the race.

So I pick D. If the question would have been "in equal time" answer were C.
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New post 05 Dec 2004, 05:07
Since this is a most question, we should start with choice E and move backwards.

Drew a chart like this:
Laticia
(Assuming answer is E - 8.5miles)
3.5 miles ---- 6 min mile - 21 min
5 miles ------- 8 min mile -- 40 min
Total = 61 min

Johanna
(Assuming answer is 8.5 miles)
8.5 miles --- 7 min mile ---- 59.5 min
since 59.5 < 61 we must choose another answer

Assuming answer is (7 miles)
Laticia
3.5 miles --- 6 min mile --- 21 min
3.5 miles ---- 8 min mile --- 28 min
Total = 49 min

Johanna
7 miles --- 7 min mile --- 49
This is the answer : D

I think GMAT doesnt test us on our formulas or even remotely medium formulaes. It usually boils down to simple addition and subtraction. They just want u to set up the addition and subtraction. Dont be confused by setting up equations. Use POE and plugging in.

:-D
  [#permalink] 05 Dec 2004, 05:07
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