Final answer:
To find the value of t when s = 12 and r = 9, set up and solve a proportion using the given information. Therefore, when s = 12 and r = 9, t = 60.
Step-by-step explanation:
To find the value of t when s = 12 and r = 9, we can use the concept of a variable that varies between two values. Given that t varies between s and r, and t = 120 when s = 15, we can set up a proportion to solve for t when s = 12 and r = 9.
We can set up the proportion as:
t / (s - r) = 120 / (15 - 9)
Substituting the values of s and r:
t / (12 - 9) = 120 / (15 - 9)
Simplifying:
t / 3 = 120 / 6
Cross-multiplying:
6t = 120 * 3
Simplifying:
6t = 360
Dividing both sides by 6:
t = 60
Therefore, when s = 12 and r = 9, t = 60.