Question

Elia rode her bicycle from her house to the beach at a constant speed of 18 kilometers per hour, and then rode from the beach to the park at a constant speed of 15 kilometers per hour the total duration of the rides was 1 hour and the distances she rode in each direction are equal. 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

Answer 1

Answer:

b+p=1 and 18b=15p

Step-by-step explanation:

Answer 2

Answer:

Elia was riding $\dfrac{5}{11}$ of an hour from the house to the beach, $\dfrac{6}{11}$ of an hour from the beach to the house and rode

$8\dfrac{2}{11}$ kilometers from the house to the beach and

$8\dfrac{2}{11}$ 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:

$\left\{\begin{array}{l}b+p=1\\ \\18b=15p\end{array}\right.$

From the first equation

$b=1-p$

Substitute it into the second equation

$18(1-p)=15p\\ \\18-18p=15p\\ \\18=18p+15p\\ \\33p=18\\ \\p=\dfrac{18}{33}=\dfrac{6}{11}\\ \\b=1-\dfrac{6}{11}=\dfrac{5}{11}$

Elia was riding $\dfrac{5}{11}$ of an hour from the house to the beach, $\dfrac{6}{11}$ of an hour from the beach to the house and rode

$18\cdot \dfrac{5}{11}=\dfrac{90}{11}=8\dfrac{2}{11}$ kilometers to the beach and

$15\cdot \dfrac{6}{11}=\dfrac{90}{11}=8\dfrac{2}{11}$ kilometers fro mthe beach to the house.