The Shady Farm Milk Company can process milk at a fixed rate of 7500 gallons/hour. The company's clients request 100,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a. m. to 6 p. m. The company starts producing at 8 a. m. and continues to work until all of the demand has been satisfied. At noon, how many gallons of milk are in the queue to be processed?

Question

Mathematics

Alan Watson

6 October, 19:30

The Shady Farm Milk Company can process milk at a fixed rate of 7500 gallons/hour. The company's clients request 100,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a. m. to 6 p. m. The company starts producing at 8 a. m. and continues to work until all of the demand has been satisfied. At noon, how many gallons of milk are in the queue to be processed?

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Nathen Campos · Answer 1

70000 gallons

Step-by-step explanation:

The total time between 8 a. m. to 6 p. m is 10 hours. The company starts producing at 8 am, therefore the time from 8 am to noon (that is 12 p. m) is 4 hours.

Since clients demand 100,000 gallons of milk over the course of one day, the demand of milk per hour = total demand per day / total time per day

Demand per hour = 100000 gallons / 10 hours = 10000 gallons per hour

Since the milk is processed at a fixed rate of 7500 gallons/hour, At noon the amount of of milk produced = 7500 gallons/hour * 4 hours = 30000 gallons.

The gallons of milk are in the queue to be processed at noon = 100000 gallons - 30000 gallons = 70000 gallons