What distance separates Hillary and Eugene when they finish?

Question

Starting at the same spot on a circular track that is 80 meters in diameter, Hillary and
Eugene run in opposite directions, at 300 meters per minute and 240 meters per minute,
respectively. They run for 50 minutes. What distance separates Hillary and Eugene when
they finish? There is more than one way to interpret the word distance in this question.

Answer 1

The definition of π is Circumference/diameter, so C = πd

         In this case, that is C = 80π meters

 

Hillary runs at 300 m/min for 50 minutes.  

That's (300 m/min)*(50 min) = 15000 m

      or 59.7 times around the track.

 

Eugene runs 240 m/min in the opposite direction for 50 minutes.

       That's (240 m/min)*(50 min) = 12000 m

         or 47.7 times around the track in the opposite direction.

 

So (draw a picture), Eugene's distance from Hillary (along the track) is:

     (0.3+0.3)*C = 0.6*C

             0.6*(80π) meters = 4.8π meters = 15.0 meters

 

The other way to calculate "how far from?" is to consider the distance directly between them (not following the track).

Answer 2

d_Hillary = (300)(50) or 15000m. That is 187 times around plus 0.5

d_Eugene = (240)(50) or 12000m That is 150 times around.

 

They are 40 m apart.