An agricultural facility uses two automated loading conveyors, Conveyor A and Conveyor B, … — GMAT

An agricultural facility uses two automated loading conveyors, Conveyor $A$ and Conveyor $B$ , to fill a grain storage silo. Working alone at its constant rate, Conveyor $A$ can fill the silo in 10 hours. Working alone at its constant rate, Conveyor $B$ can fill the silo in 15 hours. Conveyor $A$ begins filling the empty silo alone. After 4 hours, Conveyor $B$ is turned on, and both conveyors work together at their respective constant rates until the silo is completely full. How many total hours does it take, from the moment Conveyor $A$ starts, to completely fill the silo?

Cevap: 7.6 hours

Cevap

The total time required to fill the silo is 7.6 hours.

Conveyor A fills 1/10 of the silo per hour and works alone for 4 hours, completing 2/5 of the total job. The remaining 3/5 of the job is completed by both conveyors working together at a combined rate of 1/10 + 1/15 = 1/6 silo per hour. Dividing 3/5 by 1/6 gives 3.6 hours for the second stage. Adding the initial 4 hours yields a total time of 7.6 hours.

Adım Adım Çözüm

Determine the individual hourly rates of Conveyor A and Conveyor B.

Conveyor A rate =

1/10

silo per hour; Conveyor B rate =

1/15

silo per hour.

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

Calculate the fraction of the silo filled by Conveyor A working alone for 4 hours.

Work completed =

4 \times \frac{1}{10} = \frac{2}{5}

of the silo.

Work done equals rate multiplied by time.

Determine the remaining fraction of work to be completed.

Remaining work =

1 - \frac{2}{5} = \frac{3}{5}

of the silo.

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

Calculate the combined work rate when both conveyors operate together.

Combined rate =

\frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6}

silo per hour.

When working together, individual rates add up.

Determine the time required for both conveyors to finish the remaining work.

Time =

\frac{3/5}{1/6} = \frac{18}{5} = 3.6

hours.

Divide remaining work by the combined work rate.

Sum the time spent in both stages to find the total time.

Total time =

4 + 3.6 = 7.6

hours.

The total duration includes 4 hours of Conveyor A operating alone plus 3.6 hours of combined operation.

Anahtar Kavram

Work Rate and Combined Work

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru