Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Percy and Wyatt started out at their houses and are biking towards each other. Percy started out first, and has already gone 6 kilometers. He bikes at a constant speed of 4 kilometers per hour. Wyatt 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 long will that take? How far will each boy have ridden? In _____ hours, both boys will have ridden _____ kilometers.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Percy and Wyatt started out at their houses and are biking towards each other. Percy started out first, and has already gone 6 kilometers. He bikes at a constant speed of 4 kilometers per hour. Wyatt 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 long will that take? How far will each boy have ridden?   In _____ hours, both boys will have ridden _____ kilometers.

Bytelearn · Accepted Answer

Define Variables: Define the variables for the time it takes for Percy and Wyatt to meet. Let t be the time in hours it takes from now for Percy and Wyatt to meet.Equation for Percy's Distance: Write the equation for the distance Percy will have ridden. Percy has already ridden 6 kilometers and rides at a speed of 4 kilometers per hour. Distance = initial distance + speed * time Distance for Percy = 6 + 4tEquation for Wyatt's Distance: Write the equation for the distance Wyatt will have ridden. Wyatt just left and rides at a speed of 7 kilometers per hour. Distance = speed * time Distance for Wyatt = 7tEquation for Meeting Halfway: Since they meet halfway, the distances they ride must be equal. 6 + 4t = 7tSolve for t: Solve the equation for t. 6 + 4t = 7t 6 = 7t - 4t 6 = 3t t = 6 / 3 t = 2Calculate Distances: Calculate the distance each boy has ridden. For Percy: Distance = 6 + 4t = 6 + 4(2) = 6 + 8 = 14 kilometers For Wyatt: Distance = 7t = 7(2) = 14 kilometersCheck Meeting Condition: Check if the distances are equal and if they meet the condition of meeting halfway. Both distances are 14 kilometers, which means they meet halfway and the condition is satisfied.

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