A commercial bakery has two industrial ovens, Oven A and Oven B. Working alone at its cons… — GMAT

A commercial bakery has two industrial ovens, Oven A and Oven B. Working alone at its constant rate, Oven A can bake a full order of $1,800$ pastries in $6$ hours. Working alone at its constant rate, Oven B can bake the same order in $9$ hours. If Oven A begins baking the order alone and is joined by Oven B after $2$ hours, how many total hours will it take from the time Oven A starts until the full order of $1,800$ pastries is baked?

Cevap: 4.4 hours

Cevap

The total time required to complete the entire order of pastries is 4.4 hours.

The total time of 4.4 hours is derived by determining Oven A's rate (1/6 job/hour) and Oven B's rate (1/9 job/hour). In the first 2 hours, Oven A completes 1/3 of the job, leaving 2/3. Operating together, their combined rate is 5/18 job/hour, which finishes the remaining 2/3 of the job in 2.4 hours. Summing 2 hours and 2.4 hours yields 4.4 total hours.

Adım Adım Çözüm

Determine the individual work rates per hour.

Oven A completes

\frac{1}{6}

of the job per hour; Oven B completes

\frac{1}{9}

of the job per hour.

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

Calculate the fraction of work completed during the first 2 hours by Oven A.

Oven A completes

2 \times \frac{1}{6} = \frac{1}{3}

of the total job.

Work done equals rate multiplied by time spent working.

Find the remaining fraction of work to be done.

Remaining work is

1 - \frac{1}{3} = \frac{2}{3}

of the job.

Subtract the completed fraction from 1 (the whole job).

Calculate the combined rate of Oven A and Oven B working together.

Combined rate is

\frac{1}{6} + \frac{1}{9} = \frac{3}{18} + \frac{2}{18} = \frac{5}{18}

job per hour.

When entities work together, their individual rates add up.

Calculate the time spent by both ovens working together to complete the remaining work.

Time together is

\frac{2/3}{5/18} = \frac{12}{5} = 2.4

hours.

Time equals remaining work divided by the combined rate.

Calculate total time from the start.

Total time =

2 + 2.4 = 4.4

hours.

Add the initial single-agent work duration to the combined work duration.

Anahtar Kavram

Work Rate and Combined Work

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