Math  /  Algebra

QuestionWrite a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Oscar and Roger started out at their houses and are biking towards each other. Oscar started out first, and has already gone 4 kilometers. He bikes at a constant speed of 4 kilometers per hour. Roger just left, and rides at 6 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?
Oscar and Roger will have each biked \square kilometers in \square hours.

Studdy Solution
Calculate the distance each boy has ridden and the time taken:
Substitute t=2 t = 2 back into one of the distance equations to find d d : Using Roger's equation: d=6t d = 6t d=6×2 d = 6 \times 2 d=12 d = 12
So, each boy will have biked 12 kilometers.
The time taken is t=2 t = 2 hours.
Oscar and Roger will have each biked 12 \boxed{12} kilometers in 2 \boxed{2} hours.

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