Problem Solving

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

Is the answer B?

Firstly,remember whenever you see distance problems involving 90 degree directions (N-W,N-E,S-E etc) be sure that at some point you will need to apply the pythagoras theorem.

Now from the figure attatched,

Distance 0A = Rate * Time = 8 * 1/2 = 4 miles
Distance 0B = Rate * Time = 12 * 1/2 = 6 miles

Now,all the question wants us to find out is the length AB to the nearest mile!

Apply pythagoras theorem,

AB^2 = 6^2+4^2 = 52
Hence,Approximately AB would be 7 when rounded to the nearest mile.