Solve the variation problem.
-The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average speed of the swimmer if it takes 37.5 seconds to finish the race.
A)6 feet per second
B)5 feet per second
C)4 feet per second
D)3 feet per second

Question

Quizplus · Accepted Answer

The relationship between time and speed is given by $T = \frac{k}{S}$, where $T$ is the time, $S$ is the speed, and $k$ is a constant. Given $T_1 = 30$ seconds and $S_1 = 5$ feet per second, we can find $k = T_1 \times S_1 = 30 \times 5 = 150$. For $T_2 = 37.5$ seconds, we solve for $S_2$ in $37.5 = \frac{150}{S_2}$, giving $S_2 = \frac{150}{37.5} = 4$ feet per second.

Solve the Variation Problem