Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?

2.56 hr

or 2 hr 33 min.

Step-by-step explanation:

At time zero, Tommy sets off and after t seconds he arrives at A.

At time zero + 2 hrs, Zach sets off and he arrives at B at the same time as Tommy reaches A.

This means that Zach's travel time must be [t-2] hrs.

We know that distance travelled = Average speed x time taken.

So the distance travelled by Tommy = 3t

and the distance travelled by Zach = 4[t-2].

Now we can apply Pythagoras:

(3t)^2+[4(t−2)]^2=8^2

9t^2+16t2^2−32t−32t+64=64

25t^2=64t

25t=64

t=64/25

=2.56 hr