Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Zack and Pete started out at their houses and are biking towards each other. Zack started out first, and has already gone $4$ miles. He bikes at a constant speed of $3$ miles per hour. Pete just left, and rides at $4$ miles 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? $\newline$ In $\_$ hours, both boys will have ridden $\_$ miles.

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Solve a system of equations using substitution: word problems

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Zack and Pete started out at their houses and are biking towards each other. Zack started out first, and has already gone

4

miles. He bikes at a constant speed of

3

miles per hour. Pete just left, and rides at

4

miles 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?

\newline

\_

hours, both boys will have ridden

\_

miles.

Define variables: Let's define the variables for the distances each boy will have ridden when they meet. Let $x$ be the time in hours it takes for Zack and Pete to meet. Zack has already ridden $4$ miles, so the distance Zack will have ridden is $4$ miles plus $3$ miles per hour times $x$ hours. Pete has just started, so the distance Pete will have ridden is $4$ miles per hour times $x$ hours. They meet halfway between their houses, so the distances they have ridden must be equal. $\newline$ Zack's distance: $4 + 3x$ $\newline$ Pete's distance: $4x$
Set up equation: Now we can set up the equation to represent the situation where the distances are equal when they meet. $4 + 3x = 4x$
Isolate variable: To solve for $x$ , we need to isolate the variable on one side of the equation. We can do this by subtracting $3x$ from both sides of the equation. $4 + 3x - 3x = 4x - 3x$ $4 = x$
Calculate Zack's distance: Now that we have the value for $x$ , which is the time in hours it took for Zack and Pete to meet, we can calculate the distance each boy has ridden. For Zack: $\newline$ Distance ridden by Zack = $4 + 3x$ $\newline$ Distance ridden by Zack = $4 + 3(4)$ $\newline$ Distance ridden by Zack = $4 + 12$ $\newline$ Distance ridden by Zack = $16$ miles
Calculate Pete's distance: For Pete: $\newline$ Distance ridden by Pete = $4x$ $\newline$ Distance ridden by Pete = $4(4)$ $\newline$ Distance ridden by Pete = $16$ miles
Final results: We have found that it took $4$ hours for Zack and Pete to meet, and each boy has ridden $16$ miles.