A water desalination plant processes seawater using two filtration units, Unit P and Unit … — ACT

A water desalination plant processes seawater using two filtration units, Unit P and Unit Q. Unit P can process $720$ gallons of water in $45$ minutes. Unit Q processes water at a rate that is $25\%$ faster than Unit P. If both units operate continuously at their respective rates, how many total gallons of water can Unit P and Unit Q process combined in $2.5$ hours?

A
$3,000$
B
$4,200$
$5,400$ Cevap
D
$8,550$
E
$9,000$

Cevap

5,400

gallons

Unit P processes water at a rate of

16

gallons per minute (

720 \div 45

). Unit Q operates

25\%

faster, making its rate

20

gallons per minute (

16 \times 1.25

). Working simultaneously, their combined rate is

36

gallons per minute (

16 + 20

). Converting

2.5

hours into

150

minutes (

2.5 \times 60

) and multiplying by the combined rate gives a total of

36 \times 150 = 5,400

gallons.

Adım Adım Çözüm

Calculate the unit processing rate of Unit P per minute.

\frac{720 \text{ gallons}}{45 \text{ minutes}} = 16 \text{ gallons per minute}

Divide the total gallons processed by Unit P by the number of minutes to find its unit rate.

Determine the unit processing rate of Unit Q per minute.

16 \times (1 + 0.25) = 20 \text{ gallons per minute}

Unit Q is 25% faster than Unit P, so multiply Unit P's rate by 1.25.

Calculate the combined processing rate of both units.

16 + 20 = 36 \text{ gallons per minute}

Add the individual rates of Unit P and Unit Q to get their joint processing speed.

Convert 2.5 hours to minutes and calculate the combined total gallons processed.

2.5 \text{ hours} \times 60 \text{ minutes/hour} = 150 \text{ minutes}

;

36 \times 150 = 5,400 \text{ gallons}

Multiply the combined rate per minute by the total operating time in minutes.

Anahtar Kavram

Unit rate calculation and proportional scaling across multiple rate sources

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru