Noah and Owen will have each biked miles in hours.

Question

Noah and Owen started out at their houses and are biking towards each other. Noah started out first, and has already gone 1 mile. He bikes at a constant speed of 3 miles per hour. Owen just left, and rides at 4 miles per hour. When the boys meet halfway between their houses, they will continue to the park together. How far will each boy have ridden? How long will that take?

Answer 1

The problem is solved by seeing that in the same time interval t, each boy rides a different distance. 

Let the distance between their houses be d.

We are told they meet halfway between their houses. 

 

The physics here is in seeing that time = distance/speed  since by def speed = distance/time

So, we equate these different distances each boy travels 

Owen travels the full half d, d/2 in time t, but Noah has 1 mile less to travel because of his head start (d/2)-1

 

time1 = time2  is then Owen's distance/speed = Noah's distance/speed

                                                (d/2)/4         = [(d/2)-1]/3

Solve this for d/2 = 4 miles

Since Owen rides at 4 mph, it will take him 1 hour.

 

So Noah rides 1 mile head start.  He has 3 miles remaining at 3mph to meet Owen.  Owen starts late but travels faster and they meet halfway between their houses. In this 1 hour, Noah travels 3 miles and Owen travels 4 miles.