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

`\displaystyle b=0.45\ h`

`\displaystyle p=0.55\ h`

Explanation:

Cinematics

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

`\displaystyle v=(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=(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=(x)/(18)`

`\displaystyle p=(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 (x)/(18)+(x)/(15)=1`

Multiplying by 90

`\displaystyle (90x)/(18)+(90x)/(15)=90`

Simplifying and solving for x

`\displaystyle 5x+6x=90`

`\displaystyle 11x=90`

`\displaystyle x=(90)/(11)=8.18\ km`

We finally compute b and p

`\displaystyle b=(8.18)/(18)=0.45\ h`

`\displaystyle p=(8.18)/(15)=0.55\ h`