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On level farmland, two runners leave at the same time from

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On level farmland, two runners leave at the same time from [#permalink] New post   02 Jun 2007, 17:59
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9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14
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[#permalink] New post   02 Jun 2007, 18:05
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If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.

Side 1 = 8 m/h --> 4 m in 1/2 hr
Side 2 = 12 m/h --> 6 m in 1/2 hr

to complete this right angle triangle
d^2 = 4^2 + 6^2
d^2 = 52
= 2 sqrt(13) ~ 7

Answer option B
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[#permalink] New post   02 Jun 2007, 18:10
Let ABC is a right angle triangle, and angle ABC is 90 degree, So, first one is going through AB and achieved 4miles whereas the person on BC achieves 6 miles in half an hour,

Now sqrt(4^2 + 6^2) = nearest distance ~ 7 B.
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On level farmland, two runners leave at the same time from [#permalink] New post   Updated on: 18 Mar 2014, 23:38
On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after \(\frac{1}{2}\) hour ?

(A) 6
(B) 7
(C) 8
(D) 12
(E) 14

Originally posted by lanka1 on 29 Apr 2010, 05:07.
Last edited by Narenn on 18 Mar 2014, 23:38, edited 1 time in total.
Question stem corrected
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Re: farmland [#permalink] New post   29 Apr 2010, 05:47
lanka1 wrote:
On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after hour ?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14


is the question correct as none of the options seem fit??
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Re: farmland [#permalink] New post   29 Apr 2010, 06:14
We need to find root (8^2 + 12^2) = root(208)
Since 208 is closer to 196, which is 14^2, my answer is 14 miles corrected to the nearest mile.

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Re: farmland [#permalink] New post   29 Apr 2010, 08:06
1st Runner; 8mph North
2nd Runner; 1st Runner+4mph = 12mph East.

After an hr, 1st runner and 2nd runner will reach 8m and 12m respectively from the intersection they started. Because they ran North and East, their path forms a right angle and hence distance between them would be hypotenuse, which is sqrt(8*8+12*12) = sqrt(208), which is close to 14 (sqrt of 196).

Answer is E.
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   16 Mar 2014, 10:25
The answer is B since they are asking about the distance after half an hr. 14/2 = 7
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   18 Mar 2014, 13:27
Correct the question pleas
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   18 Mar 2014, 23:37
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lanka1 wrote:
On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after hour ?

(A) 6
(B) 7
(C) 8
(D) 12
(E) 14


There was an error in the question posted originally. It is actually asking for the distance between two runners after 1/2 hour travel at their respective directions. I have corrected the error. Choice B is the Answer.
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   19 Mar 2014, 20:46
Distance covered

= \(\sqrt{4^2 + 6^2}\)

= \(\sqrt{52}\)

= 7 (Approx) = Answer = B
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   02 Sep 2020, 11:42
bmwhype2 wrote:
9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14

In 1/2 HOur first runner covers 4 miles and second runner covers 6 miles

Thus, Distance between them is \(\sqrt{16 + 36} = \sqrt{52}\) ~ 7 , Answer must be (B)
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   10 Sep 2020, 03:11
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Won't nearest mile means half of hypotenuse?


Confused with the phrasing of "Nearest mile".

Posted from my mobile device
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   10 Nov 2021, 22:41
"The nearest" mile did seem confusing!!
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Re: On level farmland, two runners leave at the same time from [#permalink] New post   17 Dec 2023, 09:11
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Re: On level farmland, two runners leave at the same time from [#permalink]
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