Working alone at a constant rate, Pump A can drain a full water reservoir in 6 hours, whil… — GRE General Test

Working alone at a constant rate, Pump A can drain a full water reservoir in $6$ hours, while Pump B working alone at a constant rate can drain the same full reservoir in $4$ hours. Which of the following statements must be true? Select all such statements.

Working together, Pump A and Pump B can drain the entire reservoir in $2.4$ hours.Cevap
In $1$ hour, Pump A and Pump B working together drain $\frac{5}{12}$ of the total reservoir volume.Cevap
C
The combined rate of Pump A and Pump B working together is $\frac{1}{10}$ of the reservoir per hour.
D
Pump A's individual work rate accounts for $\frac{3}{5}$ of the combined hourly work rate of both pumps.
E
Pump B's hourly rate is $33.\overline{3}\%$ greater than Pump A's hourly rate.

Cevap

The statements confirming that the two pumps together drain the reservoir in 2.4 hours and that they drain 5/12 of the reservoir in 1 hour are correct.

The rate for Pump A is

\frac{1}{6}

job/hr and for Pump B is

\frac{1}{4}

job/hr. Their combined rate is

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

of the reservoir per hour, which directly validates the statement regarding 1 hour of combined work. Dividing

1

full reservoir by

\frac{5}{12}

yields

2.4

hours, which validates the total elapsed time statement.

Adım Adım Çözüm

Calculate individual work rates

Pump A rate =

\frac{1}{6}

reservoir/hr, Pump B rate =

\frac{1}{4}

reservoir/hr

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

Calculate combined work rate

Combined rate =

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

reservoir/hr

Rates add when workers/pumps perform simultaneously.

Calculate time needed for full task

Total time =

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

hours

Total work (

1

) divided by combined rate gives total elapsed time.

Anahtar Kavram

Combined Work Rates and Inverse Time Relationships

Tahmini Süre:1m 0s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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