SOLUTION: The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. The swimmer finishes the race in 30 seconds with the average spe

Click here to see ALL problems on test

Question 997918: The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. The swimmer finishes the race in 30 seconds with the average speed of 5 feet per second. Find the average speed of the swimmer if it takes 50 seconds to finish the race.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
inverse proportion formula is y = k/x.

first you want to find the value of k and then you want to solve using that value of k.

you are given that the swimmer finishes the race in 30 seconds with the average speed of 5 feet per second.

y is the time.
x is the rate.

you get y = k/x becomes 30 = k/5

solve for k to get k = 5*30 = 150

now you want to know the speed if the swimmer finishes the race in 50 seconds.

you get y = k/x becomes 50 = 150 / x.

solve for x to get x = 150 / 50 = 3 feet per second.

you can check you answer by using the rate * time = distance formula.

if the swimmer finishes the race in 30 seconds with an average speed of 5 feet per second, then the distance is equal to 5 * 30 = 150 feet.

if the swimmer takes 50 seconds to finish the race, then the rate * time = distance formula becomes rate * 50 = 150.

solve for rate to get rate = 150 / 50 = 3 feet per second.

the answer is confirmed as accurate using the rate * time = distance formula.

note that k turned out to be the distance.

since k is the constant of variation, the distance turned out to be the constant of variation in this problem.