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

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.

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