they will have gone 4 and 6 miles, respectively. Just do the pythagorean theorem :


4^2 + 6 ^ 2 = 52,

The square root of this is closest to 7.

grandh01 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 1/2 hour ?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14

At first I was a little confused with this question because it does not say approximately, normally the GMAT makes it very clear. Anyway, one runner is running north (we'll call him N) and the other is running east(well call him E), so they from a RIGHT triangle.

N runs at a rate of 8MPH
E runs at a rate of 12MPH (4MPH more than E)

They run for 1/2 hour so plug it in the the rate/work formula to see how far they go (Rate*Time=Distance)

N: 8*1/2 = 4
E: 12*1/2 = 6

Going back to our right triangle; one side is 4 and the other is 6. Because it is a right triangle we can find the other side by using the Pythagorean theorem. So.. 16+36 = 52.

Now here is where I thought I did something wrong because the question does not say approximately and 52 is not a perfect square. However, I check all my math and I am sure the 3rd side is the root of 52, so lets approximate. 7*7=49 and 8*8=64. 52 is CLOSER to 49 than to 64, so the answer is 7, option B.

Let me know if this helps.

combination of speed and distance with pythagorus theorem
distance travelled is half that is travelled in one hour as it is calculated for half an hour