Bert and Duncan take long walks every evening. Bert walks at a constant speed of 4 kilometers per hour, and Duncan walks at a constant speed of 5 kilometers per hour. One evening, Bert headed out first, and had already gone 2 kilometers when Duncan started his walk. How long after Duncan started his walk will they have walked the same distance? Write a system of equations, graph them, and type the solution. ____ hours

Set up Bert's equation: Let's set up the equations for Bert and Duncan's walks. Bert's equation is based on his speed and the head start he got. Since Bert walks at 4 km/h and had a 2 km head start, his distance equation is $ d = 4t + 2 $. Duncan walks faster at 5 km/h, starting later, so his equation is $ d = 5t $. Set up Duncan's equation: Now, we need to find when their distances are equal, which means setting the equations equal to each other: $ 4t + 2 = 5t $. Find when distances are equal: Solve for $ t $ by subtracting $ 4t $ from both sides: $ 2 = t $.

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Bert and Duncan take long walks every evening. Bert walks at a constant speed of $4\,\text{kilometers per hour}$ , and Duncan walks at a constant speed of $5\,\text{kilometers per hour}$ . One evening, Bert headed out first, and had already gone $2\,\text{kilometers}$ when Duncan started his walk. How long after Duncan started his walk will they have walked the same distance? $\newline$ Write a system of equations, graph them, and type the solution. $\newline$ $\_\_\_\_$ hours $\newline$

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Q. Bert and Duncan take long walks every evening. Bert walks at a constant speed of

4\,\text{kilometers per hour}

, and Duncan walks at a constant speed of

5\,\text{kilometers per hour}

. One evening, Bert headed out first, and had already gone

2\,\text{kilometers}

when Duncan started his walk. How long after Duncan started his walk will they have walked the same distance?

\newline

Write a system of equations, graph them, and type the solution.

\newline

\_\_\_\_

hours

\newline

Set up Bert's equation: Let's set up the equations for Bert and Duncan's walks. Bert's equation is based on his speed and the head start he got. Since Bert walks at $4$ km/h and had a $2$ km head start, his distance equation is $d = 4t + 2$ . Duncan walks faster at $5$ km/h, starting later, so his equation is $d = 5t$ .
Set up Duncan's equation: Now, we need to find when their distances are equal, which means setting the equations equal to each other: $4t + 2 = 5t$ .
Find when distances are equal: Solve for $t$ by subtracting $4t$ from both sides: $2 = t$ .