Question 133743
Speed of the motorcycle heading toward north = 20mi/hr
Time travelled = t hrs
so distance covered = speed x time
                      = 20 t miles

Speed of the motorcycle heading toward east = 48mi/hr
Time travelled = t hrs
so distance covered = speed x time
                      = 48 t miles

North and east are at right angles.

So applying Pythagorean theorem, the distance between them is given by,

distance = sqrt( (48t)^2 + (20t)^2 )
         = sqrt ( 2304 t^2 + 400 t^2 )
         = sqrt ( 2704 t^2 )
         = 52 t
So at the end of t hrs they are 52 t miles apart.

good luck!!!