Question

Courtney walked from her house to the beach at a constant speed of 444 kilometers per hour, and then walked from the beach to the park at a constant speed of 555 kilometers per hour. The entire walk took 222 hours and the total distance Courtney walked was 888 kilometers. Let bbb be the number of hours it took Courtney to walk from her house to the beach, and ppp 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:

Answer 1

Given:

The constant speed with which Courtney walked from her house to the beach = 4 km/hr

The constant speed with which Courtney walked from the beach to the park = 5 km/hr

Total time of the entire walk = 2 hours

Total distance Courtney walked = 8 km

To find:

Write the system of equations that represents the given situation

Solution:

"b" → no. of hours it took Courtney to walk from her house to the beach

"p" → no. of hours it took Courtney to walk from the beach to the park

We have the formula as,

$Time\:=\:\frac{Distance}{Speed}$

⇒ Distance = Time × Speed ...... (i)

Since the time taken by Courtney for the entire walk is 2 hours, we can form a linear equation as,

Equation 1 :⇒ $\boxed{b \:+\: p \:=\: 2}$

Also, the total distance walked by Courtney from house to beach and from beach to park is 8 hrs, so by using the formula in (i) we can form another linear equation as,

Equation 2 :⇒ $\boxed{4b \:+\: 5p \:=\: 8}$

Thus, the two system of equations that represent this situation are

$\boxed{b \:+\: p \:=\: 2} \:and \:\boxed{4b \:+\: 5p \:=\: 8}$.

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