Question content area topPart 1Luis and Raul

Arianna Smith

Arianna Smith

Answered question

2022-09-21


 

 

 

Question content area top

Part 1

Luis and Raul are riding their bicycles to the beach from their respective homes. Luis proposes that they leave their respective homes at the same time and plan to arrive at the beach at the same time. The diagram shows​ Luis's position at two points during his ride to the beach. Write an equation in​ slope-intercept form to represent​ Luis's ride from his house to the beach. If Raul lives 5 miles closer to the beach than​ Luis, at what speed must Raul ride for the plan to​ work?

Answer & Explanation

nick1337

nick1337

Expert2023-05-28Added 777 answers

Given that Luis proposes they leave their respective homes at the same time and plan to arrive at the beach at the same time, it implies that the time it takes for Luis to ride to the beach is the same as the time it takes for Raul to ride to the beach.
Let's assume the distance from Luis's house to the beach is represented by d. Since Raul lives 5 miles closer to the beach, Raul's distance from his house to the beach can be represented as (d5).
Let's denote the speed at which Luis rides as L (in miles per hour) and the speed at which Raul rides as R (in miles per hour).
We know that speed is equal to distance divided by time. Since the time is the same for both Luis and Raul, we can set up the following equation:
dL=d5R.
To represent Luis's ride from his house to the beach in slope-intercept form, we can rearrange the equation to solve for R:
R=Ld5·d.
In this equation, the slope is Ld5 and the y-intercept is 0.
Therefore, the equation in slope-intercept form that represents Luis's ride from his house to the beach is:
R=Ld5·d.
In order for the plan to work, Raul must ride at a speed of Ld5·d miles per hour.

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