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Zorluk: OrtaDirect Proportions

A high-capacity water pump transfers 840840 gallons of water in 1515 minutes. Operating at this exact constant rate, how many gallons of water will the pump transfer in 3.53.5 hours?

  1. A
    6060
  2. B
    196196
  3. C
    1,1761,176
  4. 11,76011,760Cevap

Cevap

The pump will transfer 11,760 gallons of water in 3.5 hours.
The problem describes a direct proportion between water volume and time. First, the unit rate is found by dividing 840840 gallons by 1515 minutes, which gives 5656 gallons per minute. Then, the target time of 3.53.5 hours is converted to 210210 minutes (3.5×603.5 \times 60). Multiplying the unit rate of 5656 gallons per minute by the 210210 minutes yields 11,76011,760 gallons.

Adım Adım Çözüm

1
Find the unit rate of the pump in gallons per minute.
840÷15=56840 \div 15 = 56 gallons per minute.
To establish a common base rate that can be scaled to any duration.
2
Convert the target time from hours to minutes.
3.5×60=2103.5 \times 60 = 210 minutes.
Proportions require consistent units across all terms; the rate is in minutes, so the target time must also be in minutes.
3
Multiply the unit rate by the total number of minutes.
56×210=11,76056 \times 210 = 11,760 gallons.
To find the total volume transferred at the constant rate over the specified time period.

Anahtar Kavram

Direct Proportions

Alternatif Yöntem

Instead of finding the unit rate per minute, you can find the rate per hour. Since 15 minutes is 1/41/4 of an hour, multiply 840 by 4 to get 3,3603,360 gallons per hour. Then, multiply 3,3603,360 by 3.53.5 hours to get 11,76011,760 gallons.
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