Question

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 w = r + rt. When solving this equation for t, which of the following steps would not be algebraically correct?

a) Add r to both sides.
b) Factor out r from the right side.
c) Divide both sides by r
d) Subtract w from both sides.

Answer 1

The incorrect step in solving the equation w = r + rt for t is adding r to both sides. The correct steps include factoring r from the right side, dividing both sides by r after factoring, and subtracting w from both sides.

Step-by-step explanation:

The equation w = r + rt shows the work accomplished by two people working at different rates (r) for the same amount of time (t). To solve for t, some algebraic manipulations are required. Let's look at the proposed steps:

• Adding r to both sides does not help isolate t and is not part of the standard process used to isolate a variable.
• Factoring out r from the right side would leave us with w = r(1 + t), which is a correct step towards isolating t.
• Dividing both sides by r, when done after factoring, is a correct step and would result in w/r = 1 + t.
• Subtracting w from both sides is indeed a required step if we want to isolate terms involving t on one side of the equation.

Therefore, the step that is not algebraically correct in solving the equation for t is adding r to both sides (Option a).