Answered

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The work accomplished by two people working on the same task for the same amount of time but at different rates is given by the equation [tex]w = r_1 t + r_2 t[/tex].

When solving this equation for [tex]t[/tex], which of the following steps would not be algebraically correct?

A. [tex]w - r_1 t = r_2 t[/tex]
B. [tex]w = t \left( r_1 + r_2 \right)[/tex]
C. [tex]w = r_1 r_2 t[/tex]

Sagot :

GinnyAnsweridn
Let's solve for [tex]\( t \)[/tex] step-by-step and identify where any algebraic errors might occur.

Given the initial equation:
[tex]\[ w = r_1 t + r_2 t \][/tex]

### Correct Step 1:
Combine like terms on the right side of the equation:
[tex]\[ w = t(r_1 + r_2) \][/tex]

### Correct Step 2:
Isolate [tex]\( t \)[/tex] by dividing both sides of the equation by [tex]\((r_1 + r_2)\)[/tex] (assuming [tex]\( r_1 + r_2 \neq 0 \)[/tex]):
[tex]\[ t = \frac{w}{r_1 + r_2} \][/tex]

### Incorrect Step:
In the given list of steps, the step:
[tex]\[ w = r_1 r_2 t \][/tex]
is algebraically incorrect.

The term [tex]\( r_1 r_2 t \)[/tex] does not correctly represent combining the rates [tex]\( r_1 \)[/tex] and [tex]\( r_2 \)[/tex] when both are working together for the same time duration [tex]\( t \)[/tex]. Instead, [tex]\( w \)[/tex] should be expressed as [tex]\( t(r_1 + r_2) \)[/tex], not [tex]\( r_1 r_2 t \)[/tex].

Therefore, the incorrect step in solving the equation for [tex]\( t \)[/tex] is:
[tex]\[ w = r_1 r_2 t \][/tex]
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