Question

If s varies directly as r and inversely as t and s=10 when r=5 and t=3, for what value of t will s=3 when r=4?

Answer 1

`t=8`

Explanation:

`"the initial statement is " spropr/t`

`"to convert to an equation multiply by k the constant of"`
`"variation"`

`rArrs=kxxr/t=(kr)/t`

`"to find k use the condition given"`

`s=10" when "r=5" and "t=3`

`s=(kr)/trArrk=(st)/r=(10xx3)/5=6`

`"the equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(s=(6r)/t)color(white)(2/2)|)))`

`s=3" when "r=4`

`s=(6r)/t`

`rArrt=(6r)/s=(6xx4)/3=8`