Graduate Management Admission Test (GMAT) Practice Test

For combined work questions involving two workers, what is the formula for total time?

1. T = (A + B)/AB

2. T = (AB)/(A + B)

3. T = (A + B)/A

4. T = AB/(A - B)

The correct answer is: T = (AB)/(A + B)

The formula for total time when two workers are combining their efforts is derived from their individual work rates. If we denote the time it takes for the first worker to complete a task as A and the time it takes for the second worker as B, their rates of work can be expressed as follows: the first worker completes \( \frac{1}{A} \) of the task per hour, while the second worker completes \( \frac{1}{B} \) of the task per hour. When working together, their combined work rate is the sum of their individual rates, which is expressed as: \[ \text{Combined Rate} = \frac{1}{A} + \frac{1}{B} = \frac{B + A}{AB} \] To find the total time (T) taken for the two workers to finish one entire task together, we take the reciprocal of their combined rate: \[ T = \frac{1}{\text{Combined Rate}} = \frac{1}{\left( \frac{B + A}{AB} \right)} = \frac{AB}{A + B} \] Thus, option B, which states that total time \( T = \frac{