Represents the following phrase
1 answer:
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Answer:
The system of equations represents this situation is:
4<em>b</em> + 5<em>p </em>= 8 and <em>b</em> + <em>p</em> = 2.
Step-by-step explanation:
The question is:
Courtney walked from her house to the beach at a constant speed of 4 kilometres per hour, and after beach to the park at a constant speed of 5 kilometres per hour. The entire walk took 2 hours and the total distance Courtney traveled was 8 kilometres. Let b be the number of hours it took Courtney to walk from her house to the beach and let p be the number of hours it took him to walk from the beach to the park. Which system of equations represents this situation?
Solution:
The formula to speed is:
Then the formula of distance traveled is:
Let the two distances traveled by Courtney be, <em>d</em>₁ and <em>d</em>₂.
It is provided that:
Speed at Courtney walked from her house to the beach was, <em>s</em>₁ = 4 km/h.
Speed at Courtney walked from the beach to the park was, <em>s</em>₂ = 5 km/h.
The total distance traveled is,
<em>d</em>₁ + <em>d</em>₂ = 8...(i)
It is assumed that,
<em>b</em> = number of hours it took Courtney to walk from her house to the beach
<em>p</em> = number of hours it took him to walk from the beach to the park
Then the equation (i) can be written as:
<em>bs</em>₁ + <em>ps</em>₂ = 8
⇒ 4<em>b</em> + 5<em>p </em>= 8
Also the total time it took to travel 8 kilometres is 2 hours.
Then,
Thus, the system of equations represents this situation is:
4<em>b</em> + 5<em>p </em>= 8 and <em>b</em> + <em>p</em> = 2.