Questions: Solve the equation for the indicated variable. 1/c + 1/5 = 1/t for t

Transcript text: Solve the equation for the indicated variable. \[ \frac{1}{c}+\frac{1}{5}=\frac{1}{t} \text { for } t \]

Solution

Solution Steps

To solve the equation \(\frac{1}{c} + \frac{1}{5} = \frac{1}{t}\) for \(t\), we need to isolate \(t\) on one side of the equation. This can be done by taking the reciprocal of both sides after combining the fractions on the left-hand side.

Step 1: Rewrite the Equation

We start with the equation: \[ \frac{1}{c} + \frac{1}{5} = \frac{1}{t} \]

Step 2: Combine the Left Side

We can express the left side with a common denominator: \[ \frac{5 + c}{5c} = \frac{1}{t} \]

Step 3: Take the Reciprocal

Taking the reciprocal of both sides gives us: \[ t = \frac{5c}{5 + c} \]

Final Answer

Thus, the solution for \(t\) is: \[ \boxed{t = \frac{5c}{c + 5}} \]

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