# 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?

##### 1 Answer

Jul 14, 2017

#### Answer:

#### 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#