Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Eli and Philip started out at their houses and are biking towards each other. Eli started out first, and has already gone 4 kilometers. He bikes at a constant speed of 3 kilometers per hour. Philip just left, and rides at 7 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? How long will that take?
Eli and Philip will have each biked ____ kilometers in ____ hours.
+130085 We know that Eli as already traveled 4 km when Philip starts
And Eli has taken 4/3 hrs to do this
So....let the time it takes Philip to reach the halway point = T (in hrs)
So....the distance Philip travels = 7T
And the distance that Eli travels = the 4 km he has traveled plus his rate times the time it takes Philip to reach the halfway point = 4 km + 3T
So....the distance that Eli travels = the distance that Philip travels ...so we have
4 + 3T = 7T
4 = 4T
T = 1 hr
So....Philip travels 7(1) = 7 km
And Eli travels 4 + 3(1) = 7 km
So...each travels 7km
It takes Eli (4/3)hrs + 1 hr = 7/3 hrs to travel halfway
And it takes Philip just 1 hour to travel halfway
