A commercial bakery uses two automated ovens, Oven X and Oven Y, to bake identical orders … — GRE General Test

A commercial bakery uses two automated ovens, Oven X and Oven Y, to bake identical orders of bread. Working alone at its constant rate, Oven X bakes a full order of bread in $8$ hours, while Oven Y, working alone at its constant rate, bakes the same order in $12$ hours. Both ovens begin baking a full order together at 8:00 a.m. At 10:00 a.m., Oven X shuts down due to a maintenance alert, and Oven Y continues working alone at its constant rate until the order is completed. How many total hours, from 8:00 a.m. until completion, does it take to finish the order?

Answer: 9 hours

Answer

The total time required from 8:00 a.m. to complete the order is

9

hours.

Working together for

2

hours at a combined rate of

\frac{1}{8} + \frac{1}{12} = \frac{5}{24}

per hour completes

\frac{5}{12}

of the order. The remaining

\frac{7}{12}

of the order takes Oven Y

7

hours to complete at its rate of

\frac{1}{12}

per hour. Adding the initial

2

hours gives a total time of

9

hours.

Step-by-Step Solution

Determine the individual hourly work rates.

Oven X completes

\frac{1}{8}

of the job per hour, and Oven Y completes

\frac{1}{12}

of the job per hour.

Work rate is the reciprocal of the total time required to complete one full job.

Calculate the fraction of the job completed in the first

2

hours.

Combined rate is

\frac{1}{8} + \frac{1}{12} = \frac{5}{24}

job per hour. In

2

hours, they complete

2 \times \frac{5}{24} = \frac{5}{12}

of the job.

Both ovens work simultaneously for

2

hours before Oven X stops.

Determine the remaining fraction of the job.

1 - \frac{5}{12} = \frac{7}{12}

of the job remains.

The full order represents

1

whole unit of work.

Find the additional time required for Oven Y to finish the remaining job alone.

\text{Time} = \frac{7/12}{1/12} = 7

hours.

Time equals remaining work divided by Oven Y's individual work rate.

Calculate the total time elapsed from start to completion.

2 + 7 = 9

hours.

The total time includes the

2

hours of combined work plus the

7

hours Oven Y worked alone.

Key Concept

Combined Work Rates and Modeling Staggered Work

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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