Question

Elia rode her bicycle from her house to the beach at a constant speed of

18
1818 kilometers per hour, and then rode from the beach to the park at a constant speed of
15
1515 kilometers per hour. The total duration of the rides was
1
11 hour and the distances she rode in each direction are equal.

Answer 1

​

b+p=1

18b=15p

​

Explanation:

Answer 2

`p=(6)/(11)\ h`

`b=(5)/(11)\ h`

The distance from the house to the beach that is the same distance from the beach to the park is
`8(2)/(11)\ km`

Explanation:

The correct question is

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.

Find the values of p and p

Let

b ----> the number of hours it took Elia to ride from her house to the beach

p ---> the number of hours it took Elia to ride from the beach to the park

we know that

The speed is equal to divide the distance by the time

so

The distance is equal to multiply the speed by the time

`b+p=1`

`b=1-p` ----> equation A

`18b=15p` ----> equation B

Solve the system by substitution

Substitute equation A in equation B and solve for p

`18(1-p)=15p`

`18-18p=15p`

`18p+15p=18`

`33p=18`

`p=(18)/(33)`

Simplify

`p=(6)/(11)\ h`

Find the value of b

`b=1-p`

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

Find the distance from the house to the beach that is the same distance from the beach to the park

`18b=18((5)/(11))=(90)/(11)\ km`

Convert to mixed number

`(90)/(11)\ km=(88)/(11)+(2)/(11)=8(2)/(11)\ km`