Solve the 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 37.5 seconds with an average speed of 4 feet per second. Find the
Average speed of the swimmer if it takes him 25 seconds to finish the race.
A) 7 ft/sec
B) 5 ft/sec
C) 6 ft/sec
D) 8 ft/sec

Question

Quizplus · Accepted Answer

Let's use the formula for inverse proportionality:

time * speed = constant

We are given that when the swimmer finishes the race in 37.5 seconds, the average speed is 4 feet per second. So we can write:

37.5 * 4 = constant

Simplifying:

150 = constant

Now we can use this constant to find the average speed when the swimmer finishes the race in 25 seconds:

25 * speed = 150

Simplifying:

speed = 150/25 = 6

Therefore, the average speed of the swimmer is 6 feet per second. The best choice is C. Let t be the time it takes to swim the race and s be the average speed of the swimmer.

According to the problem, we have:

t = k/s

where k is a constant of proportionality.

Using the first given condition, when t = 37.5 seconds and s = 4 ft/sec, we have:

37.5 = k/4

k = 150

So the equation becomes:

t = 150/s

Using the second given condition, when t = 25 seconds, we have:

25 = 150/s

s = 150/25 = 6 ft/sec

Therefore, the answer is C, 6 ft/sec.

Solve the Problem. -The Amount of Time It Takes a Swimmer to Swim