Solve for t S=1/2(V_0+V_1)t

$S = \frac{1}{2} (V_{0} + V_{1}) t$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot ((V_{0} + V_{1}) t) = S$ .

$\frac{1}{2} \cdot ((V_{0} + V_{1}) t) = S$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot ((V_{0} + V_{1}) t)) = 2 S$

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot ((V_{0} + V_{1}) t))$ .

Apply the distributive property.

$2 (\frac{1}{2} \cdot (V_{0} t + V_{1} t)) = 2 S$

Apply the distributive property.

$2 (\frac{1}{2} (V_{0} t) + \frac{1}{2} (V_{1} t)) = 2 S$

Multiply $\frac{1}{2} (V_{0} t)$ .

Combine $V_{0}$ and $\frac{1}{2}$ .

$2 (\frac{V_{0}}{2} t + \frac{1}{2} (V_{1} t)) = 2 S$

Combine $\frac{V_{0}}{2}$ and $t$ .

$2 (\frac{V_{0} t}{2} + \frac{1}{2} (V_{1} t)) = 2 S$

Multiply $\frac{1}{2} (V_{1} t)$ .

Combine $V_{1}$ and $\frac{1}{2}$ .

$2 (\frac{V_{0} t}{2} + \frac{V_{1}}{2} t) = 2 S$

Combine $\frac{V_{1}}{2}$ and $t$ .

$2 (\frac{V_{0} t}{2} + \frac{V_{1} t}{2}) = 2 S$

Apply the distributive property.

$2 \frac{V_{0} t}{2} + 2 \frac{V_{1} t}{2} = 2 S$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{V_{0} t}{2} + 2 \frac{V_{1} t}{2} = 2 S$

Rewrite the expression.

$V_{0} t + 2 \frac{V_{1} t}{2} = 2 S$

Cancel the common factor of $2$ .

Cancel the common factor.

$V_{0} t + 2 \frac{V_{1} t}{2} = 2 S$

Rewrite the expression.

$V_{0} t + V_{1} t = 2 S$

Step 4

Factor $t$ out of $V_{0} t + V_{1} t$ .

Factor $t$ out of $V_{0} t$ .

$t V_{0} + V_{1} t = 2 S$

Factor $t$ out of $V_{1} t$ .

$t V_{0} + t V_{1} = 2 S$

Factor $t$ out of $t V_{0} + t V_{1}$ .

$t (V_{0} + V_{1}) = 2 S$

Step 5

Divide each term in $t (V_{0} + V_{1}) = 2 S$ by $V_{0} + V_{1}$ and simplify.

Divide each term in $t (V_{0} + V_{1}) = 2 S$ by $V_{0} + V_{1}$ .

$\frac{t (V_{0} + V_{1})}{V_{0} + V_{1}} = \frac{2 S}{V_{0} + V_{1}}$

Simplify the left side.

Cancel the common factor of $V_{0} + V_{1}$ .

Cancel the common factor.

$\frac{t (V_{0} + V_{1})}{V_{0} + V_{1}} = \frac{2 S}{V_{0} + V_{1}}$

Divide $t$ by $1$ .

$t = \frac{2 S}{V_{0} + V_{1}}$

Solve for t S=1/2(V_0+V_1)t

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