To solve the equation [tex]\( w = t(r_1 + r_2) \)[/tex] for [tex]\( t \)[/tex], we need to isolate [tex]\( t \)[/tex] on one side of the equation. Let's go through the steps in detail:
1. Start with the given equation:
[tex]\[
w = t(r_1 + r_2)
\][/tex]
2. Isolate [tex]\( t \)[/tex] by dividing both sides of the equation by [tex]\( (r_1 + r_2) \)[/tex]:
[tex]\[
\frac{w}{r_1 + r_2} = \frac{t(r_1 + r_2)}{r_1 + r_2}
\][/tex]
3. Simplify the right side of the equation:
Since [tex]\( (r_1 + r_2) \)[/tex] appears in both the numerator and the denominator on the right side, they cancel out:
[tex]\[
\frac{w}{r_1 + r_2} = t
\][/tex]
4. Thus, the solution for [tex]\( t \)[/tex] is:
[tex]\[
t = \frac{w}{r_1 + r_2}
\][/tex]
Therefore, the correct formulation solving for [tex]\( t \)[/tex] is:
[tex]\[
t = \frac{w}{r_1 + r_2}
\][/tex]
This is the correct solution for the given equation [tex]\( w = t(r_1 + r_2) \)[/tex].
