SOLUTION: 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 200 seconds with an average speed

Algebra ->  Rational-functions -> SOLUTION: 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 200 seconds with an average speed       Log On


   

Question 1177223: 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 200 seconds with an average speed of 3 feet per second. Find the average speed of the swimmer if it takes 120 seconds to finish the race.
A)6 feet per second B)7 feet per second C)4 feet per second D)5 feet per second
Found 4 solutions by mananth, josgarithmetic, Boreal, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

+t%28alpha%29+%281%2Fs%29+ s = average speed
t= k/s
200=k/3
k=600
120 = 600/s
s= 600/120
s= 5

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
t, time
r, "speed" average
k, proportionality constant


-------------------------------------------------------------
amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer.
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t=k%281%2Fr%29

t=k%2Fr

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swimmer finishes a race in 200 seconds with an average speed of 3 feet per second.
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t%2Ar=k

k=200%2A3

k=600

The model becomes highlight%28t=600%2Fr%29.
You could do the questions using this formula.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
T=k/S
200=k/3
k=600
-
120=600/S
S=5 feet per second

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Using the formal definition of inverse proportion, the time t and the speed s are related by

t+=+k%2Fs

where k is the constant of proportionality.

All three responses you have received to this point use that constant k in one way or another to solve the problem.

For quick computation, however, it is easier to work with this equivalent statement of inverse proportion:

t%2As+=+k

That form of the statement for inverse proportion says that the product of time and speed is a constant, so there is no need to determine the proportionality constant, or to use it in your computations. You can solve the problem (or any similar problem involving inverse proportion) using the idea that the product of the time and speed for one swimmer is equal to the product of the time and speed for the other swimmer.

Then the whole problem becomes just this:

200%2A3+=+120%2Ax
600+=+120x
x+=+5

ANSWER: 5 feet per second