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 distance 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 put p the number of hours it took her to ride from the beach to the park.

Answer 1

Answer:

$\displaystyle b=0.45\ h$

$\displaystyle p=0.55\ h$

Step-by-step explanation:

Cinematics

When an object moves at a constant speed, it can be computed as

$\displaystyle v=\frac{x}{t}$

Where x is the distance traveled and t the time needed to complete it at the constant speed v

If we wanted to compute t from the equation above, then

$\displaystyle t=\frac{x}{v}$

Elia rode her bicycle from her house to the beach at 18 km/h and then from the beach to the park at 15 km/h, taking 1 hour in the whole travel, each distance being equal. If we call b as 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, then we can compute

$\displaystyle b=\frac{x}{18}$

$\displaystyle p=\frac{x}{15}$

The question doesn't ask for something in particular, so I'm helping you by solving the complete problem. We know the total time is 1 hour, so

$\displaystyle b+p=1$

Replacing b and p

$\displaystyle \frac{x}{18}+\frac{x}{15}=1$

Multiplying by 90

$\displaystyle \frac{90x}{18}+\frac{90x}{15}=90$

Simplifying and solving for x

$\displaystyle 5x+6x=90$

$\displaystyle 11x=90$

$\displaystyle x=\frac{90}{11}=8.18\ km$

We finally compute b and p

$\displaystyle b=\frac{8.18}{18}=0.45\ h$

$\displaystyle p=\frac{8.18}{15}=0.55\ h$