Worker A can complete a specific publishing task alone in 4 hours, while Worker B can comp… — GMAT

Worker A can complete a specific publishing task alone in $4$ hours, while Worker B can complete the exact same task alone in $6$ hours. Working together continuously at their respective constant individual rates, how many hours will it take both workers to complete one such task?

$2.4$ Cevap
B
$5.0$
C
$10.0$
D
$12.0$
E
$2.0$

Cevap

The combined time required to complete the task is

2.4

hours.

The correct response calculates each worker's hourly rate of completion (one-fourth and one-sixth of the job per hour), sums them to find a combined rate of five-twelfths of the job per hour, and takes the reciprocal to find that the total time required is

2.4

hours.

Adım Adım Çözüm

Determine individual work rates per hour.

Worker A's rate is

\frac{1}{4}

of the task per hour; Worker B's rate is

\frac{1}{6}

of the task per hour.

Work rate is defined as the reciprocal of total time required to complete one unit of work.

Sum the individual rates to find the combined work rate.

Combined Rate =

\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}

task per hour.

When working together, rates add together linearly.

Calculate total time by taking the reciprocal of the combined rate.

Time =

\frac{1}{\text{Combined Rate}} = \frac{12}{5} = 2.4

hours.

Time equals total work (1 unit) divided by the combined rate.

Anahtar Kavram

Combined Work Rates

Tahmini Süre:1m 0s

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