Question

A quantity, t, varies inversely with a quantity, r. If t = 6, then r = 5. What is the constant of variation? k = What is the equation that represents this variation? rt = What is the value of t when r = 15?

Answer 1

If  quantity t varies inversely with a quantity r ,
Then mathematically t α 1/r,
Introducing a constant, t = k/r .
When t = 6 then r = 5,
therefore, 6 = k/5
                 k = 6×5
                  k = 30   (Constant of variation)       
 Which means the equation connecting t and r will be t = 30/r
To find the value of t when r = 15, we use the equation of this variation
such that, t = 30/15
                 t = 2