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?

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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?

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Answer 1 · 2017-07-14T19:32:10

$t = 8$ $t=8$

Explanation:

$the initial statement is s \propto \frac{r}{t}$ $"the initial statement is " spropr/t$

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

$\Rightarrow s = k \times \frac{r}{t} = \frac{k r}{t}$ $rArrs=kxxr/t=(kr)/t$

$to find k use the condition given$ $"to find k use the condition given"$

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

$s = \frac{k r}{t} \Rightarrow k = \frac{s t}{r} = \frac{10 \times 3}{5} = 6$ $s=(kr)/trArrk=(st)/r=(10xx3)/5=6$

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

$s=3" when "r=4$

$s=(6r)/t$

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

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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

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