Data Pipeline A can process a standard batch of records in 12 hours, while Data Pipeline B… — GMAT

Data Pipeline A can process a standard batch of records in $12$ hours, while Data Pipeline B can process the same batch of records in $18$ hours. Data Pipeline A begins processing a batch alone and operates for $4$ hours before Data Pipeline B is brought online to assist. Both pipelines then continue processing together at their respective constant rates until the batch is completely processed. What is the total time, in hours, required to process the entire batch of records from start to finish?

A
$4.8$
B
$6.4$
$8.8$ Cevap
D
$15.0$
E
$24.0$

Cevap

8.8

hours (or

8\frac{4}{5}

hours)

The rate of Pipeline A is

\frac{1}{12}

per hour, so in

4

hours it completes

4 \times \frac{1}{12} = \frac{1}{3}

of the job. The remaining

\frac{2}{3}

of the job is completed by both pipelines working together. Their combined rate is

\frac{1}{12} + \frac{1}{18} = \frac{5}{36}

per hour. The time required for the joint phase is

\frac{2/3}{5/36} = 4.8

hours. Adding the initial

4

hours gives a total time of

8.8

hours.

Adım Adım Çözüm

Calculate the work completed by Data Pipeline A alone during the first

4

hours.

Pipeline A's rate is

\frac{1}{12}

batch/hour. Work done in

4

hours =

4 \times \frac{1}{12} = \frac{1}{3}

of the batch.

Determining the completed portion establishes how much work remains for the combined phase.

Determine the remaining fraction of work to be done.

Remaining work =

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

of the batch.

The combined pipelines only need to finish the remaining portion of the job.

Calculate the combined processing rate of both pipelines.

Combined rate =

\frac{1}{12} + \frac{1}{18} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36}

batch/hour.

Rates add when entities work simultaneously on the same task.

Calculate the time required for both pipelines to finish the remaining work together.

Joint time =

\frac{\text{Remaining Work}}{\text{Combined Rate}} = \frac{2/3}{5/36} = \frac{2}{3} \times \frac{36}{5} = \frac{24}{5} = 4.8

hours.

Dividing remaining work by the combined rate gives the duration of the second phase.

Calculate total time from start to finish.

Total time =

4 \text{ hours (phase 1)} + 4.8 \text{ hours (phase 2)} = 8.8

hours.

Summing both phase durations gives the total time required for the entire process.

Anahtar Kavram

Work Rate and Combined Work

Tahmini Süre:2m 0s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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