Question

courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. the entire walk took 2 hours and the total distance courtney walked was 8.5 kilometers. let b be the number of hours it took courtney to walk from her house to the beach, and p the number of hours it took her to walk from the beach to the park. which system of equations represents this situation? choose 1 answer:

Explanation:

Step1: Set up time - related equation

The total time of the walk is 2 hours. Since $b$ is the time from house to beach and $p$ is the time from beach to park, we have $b + p=2$.

Step2: Set up distance - related equation

The distance formula is $d = vt$ (distance = speed×time). The speed from house to beach is 4 km/h and time is $b$ hours, so distance is $4b$. The speed from beach to park is 5 km/h and time is $p$ hours, so distance is $5p$. The total distance is 8.5 km. So, $4b + 5p=8.5$.

Answer:

$$\begin{cases}b + p=2\\4b + 5p=8.5\end{cases}$$