Question

Joseph and Wilson each started out at their own houses and are biking towards each other. ​ ​Joseph started out first, and has already gone 10 kilometers. He bikes at a constant speed of 7 kilometers per hour. ​Wilson just left, and rides at 9 kilometers per hour. ​ ​When the boys meet halfway between their houses, they will continue to the park together. ​ ​How far will each boy have ridden to meet the other halfway? ​How long will that take?

Answer 1

Distance to halfway point=45 km

Wilson's Time=5hrs

Joseph's time=6.26hrs

Explanation:

-Let x be the number of hours it takes for the two to meet halfway when Wilson starts his ride.

#The time already utilized prior to Wilson's start is:

`Speed=(Distance)/(Time)\\\\Time=(10)/(7)\\\\=(10)/(7)\ hrs`

Joseph's remaining distance to the hallway point is less by 10km

Since, the distance to meet is equal, we equate their times as:

`Time=(Distance)/(Speed)\\\\(d-10)/(7)=(d)/(9)\\\\9d-90=7d\\\\2d=90\\\\d=45\ km\\\\(d-10)=35\ km`

Hence, the distance ridden by each to the halfway point is 45 km

#We now use this distance to solve for individual times:

`Time=(Distance)/(Speed)\\\\\#Joseph\\\\T_j=(10)/(7)+(35)/(7)\\\\=6(3)/(7)\ hrs \ or \ 6.26\ hrs\\\\\#Wilson\\\\T_w=(45)/(9)\\\\=5\ hrs`

Hence, Joseph takes 6.26hrs while Wilson takes 5hrs to get to the halfway point.