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

Question

1 month ago

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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

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-03-04T00:01:14+03:00

AnnZ [12.3K]1 month ago

7 0

Solution:

b+p=1 and 18b=15p

Detailed breakdown:

Svet_ta [12.7K] · Answer 2 · 2026-03-04T00:02:54+03:00

Answer:

Elia took $\dfrac{5}{11}$ hour to cycle from her residence to the beach, $\dfrac{6}{11}$ hour to return, and traveled

$8\dfrac{2}{11}$ kilometers from her home to the beach and

$8\dfrac{2}{11}$ kilometers on her way back.

Step-by-step explanation:

1. Let b represent the hours Elia spent cycling to the beach, and p the time taken for the return trip to the park. The combined time for both rides equals 1 hour, represented as

b + p = 1

2. With a constant speed of 18 km/h on her way to the beach, in b hours, she covered 18b kilometers. She then rode back from the beach to the park at a steady speed of 15 km/h, which amounted to 15p kilometers.

Since the distances for both trips are identical, we establish

18b = 15p

3. Solve the two equations:

$\left\{\begin{array}{l}b+p=1\\ \\18b=15p\end{array}\right.$

Using the first equation

$b=1-p$

Insert this solution into the second equation

$18(1-p)=15p\\ \\18-18p=15p\\ \\18=18p+15p\\ \\33p=18\\ \\p=\dfrac{18}{33}=\dfrac{6}{11}\\ \\b=1-\dfrac{6}{11}=\dfrac{5}{11}$

Elia took $\dfrac{5}{11}$ hour to cycle to the beach, $\dfrac{6}{11}$ hour on her return, and covered

$18\cdot \dfrac{5}{11}=\dfrac{90}{11}=8\dfrac{2}{11}$ kilometers going to the beach and

$15\cdot \dfrac{6}{11}=\dfrac{90}{11}=8\dfrac{2}{11}$ kilometers returning to her home.