Answer:
Elia was riding [tex]\dfrac{5}{11}[/tex] of an hour from the house to the beach, [tex]\dfrac{6}{11}[/tex] of an hour from the beach to the house and rode
[tex]8\dfrac{2}{11}[/tex] kilometers from the house to the beach and
[tex]8\dfrac{2}{11}[/tex] kilometers from the beach to the house.
Step-by-step explanation:
1. Let b be the number of hours it took Elia to ride from her house to the beach, and p the number of hours it took her to ride from the beach to the park. The total duration of the rides was 1 hour, so
b + p = 1
2. Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, she was riding for b hour, then she rode 18b kilometers from her house to the beach.
Elia rode from the beach to the park at a constant speed of 15 kilometers per hour, she was riding for p hours, then she rode 15p kilometers from the beach to the house.
The distances she rode in each direction are equal, so
18b = 15p
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}b+p=1\\ \\18b=15p\end{array}\right.[/tex]
From the first equation
[tex]b=1-p[/tex]
Substitute it into the second equation
[tex]18(1-p)=15p\\ \\18-18p=15p\\ \\18=18p+15p\\ \\33p=18\\ \\p=\dfrac{18}{33}=\dfrac{6}{11}\\ \\b=1-\dfrac{6}{11}=\dfrac{5}{11}[/tex]
Elia was riding [tex]\dfrac{5}{11}[/tex] of an hour from the house to the beach, [tex]\dfrac{6}{11}[/tex] of an hour from the beach to the house and rode
[tex]18\cdot \dfrac{5}{11}=\dfrac{90}{11}=8\dfrac{2}{11}[/tex] kilometers to the beach and
[tex]15\cdot \dfrac{6}{11}=\dfrac{90}{11}=8\dfrac{2}{11}[/tex] kilometers fro mthe beach to the house.
