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

b+p=1 and 18b=15p

Explanation:

Answer 2

Elia was riding
`(5)/(11)` of an hour from the house to the beach,
`(6)/(11)` of an hour from the beach to the house and rode

`8(2)/(11)` kilometers from the house to the beach and

`8(2)/(11)` kilometers from the beach to the house.

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=(18)/(33)=(6)/(11)\\ \\b=1-(6)/(11)=(5)/(11)`

Elia was riding
`(5)/(11)` of an hour from the house to the beach,
`(6)/(11)` of an hour from the beach to the house and rode

`18\cdot (5)/(11)=(90)/(11)=8(2)/(11)` kilometers to the beach and

`15\cdot (6)/(11)=(90)/(11)=8(2)/(11)` kilometers fro mthe beach to the house.