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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.

 Jan 19, 2019
 #1
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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

 

 

cool cool cool

 Jan 19, 2019
edited by CPhill  Jan 19, 2019

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