Respuesta :
Answer:
[tex]p=\frac{6}{11}\ h[/tex]
[tex]b=\frac{5}{11}\ h[/tex]
The distance from the house to the beach that is the same distance from the beach to the park is [tex]8\frac{2}{11}\ km[/tex]
Step-by-step 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
[tex]b+p=1[/tex]
[tex]b=1-p[/tex] ----> equation A
[tex]18b=15p[/tex] ----> equation B
Solve the system by substitution
Substitute equation A in equation B and solve for p
[tex]18(1-p)=15p[/tex]
[tex]18-18p=15p[/tex]
[tex]18p+15p=18[/tex]
[tex]33p=18[/tex]
[tex]p=\frac{18}{33}[/tex]
Simplify
[tex]p=\frac{6}{11}\ h[/tex]
Find the value of b
[tex]b=1-p[/tex]
[tex]b=1-\frac{6}{11}=\frac{5}{11}\ h[/tex]
Find the distance from the house to the beach that is the same distance from the beach to the park
[tex]18b=18(\frac{5}{11})=\frac{90}{11}\ km[/tex]
Convert to mixed number
[tex]\frac{90}{11}\ km=\frac{88}{11}+\frac{2}{11}=8\frac{2}{11}\ km[/tex]
