SOLUTION: A person runs n times around a circular track whose radius is t miles. For every mile that he runs, he consumes s quarts of sports drink. How will he only need 1 quart ? Unsur

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Question 1202815: A person runs n times around a circular track whose radius is t miles. For every mile that he runs, he consumes s quarts of sports drink. How will he only need 1 quart ?
Unsure how to solve.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


radius of the track in miles: t

circumference of the track in miles: 2(pi)t

distance in miles around the track n times: (2(pi)t)n = 2(pi)(t)(n)

quarts of a sports drink consumed, at s quarts per mile: 2(pi)(t)(n)(s)

If he only needs 1 quart, then

2(pi)(t)(n)(s) = 1

Of course an infinite number of different combinations of t, n, and s will have him consuming 1 quart of sports drink.

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
One time around the track circumference of 2t%2Apimiles.

n times around the track, 2tn%2Api miles.

He consumes s quarts of drink for each 1 mile of travel.

He must travel just 1 mile!
s=1

2tn%2Api=1-----------Two variables so there are some choices here.
Do you expect only whole numbers for n?
"Yes";

Then there you go. n=1, and solve for t.
n=2, and solve for t.
n=3, and solve for t.
.
.
Also think what is practical for values of t. Does each "circular" track circumference make sense?