Question

One athlete runs around Track S 3 times and Track T 4 times, running a total of 12 miles

Another athlete runs around Track S 1 time and Track T 6 times, running a total of 11 miles

What is the length of Track S in miles

Answer 1

The length of Track S is 2 miles.

Explanation:

Let the length of track S be s miles and, of T, be t miles.

Then we have the system:

3s + 4t = 12........ A

s + 6t = 11.............B Multiply this equation by -3:

-3s - 18t = -33

Adding this last equation to equation A:

0 - 14t = -21

t = -21/-14

t = 1.5

Now substitute for t in equation B:

s + 6 *1.5 = 11

s + 9 = 11

s = 2.