Question

select the correct answer.

bartolo is running a race. he determines that if he runs at an average speed of 15 feet/second, he can finish the race in 6 seconds. if he runs at an average speed of 18 feet/second, he can finish the race in 5 seconds.

what is the constant of proportionality in this inverse variation?

75
90
96
108

Explanation:

Set up the inverse variation equation

$$ y = \frac{k}{x} \implies k = x \cdot y $$

Calculate the constant of proportionality

$$ k = 15 \text{ feet/second} \times 6 \text{ seconds} = 90 $$

Verify with the second data point

$$ k = 18 \text{ feet/second} \times 5 \text{ seconds} = 90 $$

Answer:

• (A) 75
• (B) 90 (Correct answer)
• (C) 96
• (D) 108