The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it. Flow rate, x (gal/hr) Time, y (hours) 60 300 45 400 36 500 30 600 How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

Question

Mathematics

Angela Bartlett

19 December, 00:14

The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it. Flow rate, x (gal/hr) Time, y (hours) 60 300 45 400 36 500 30 600 How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

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Answers (1)

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Chef · Answer 1

Flow rate, x (gal/hr) Time, y (hours)

60 300

45 400

36 500

30 600

From those data, you conclude that the volume of water is 18,000 galons:

60 * 300 = 45 * 400 = 36 * 500 = 30 * 600 = 18,000

How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

The total speed of filling is 40 gal/h + 60gal/h = 100 gal/h

Then, you must do 18,000 gal / (100 gal/h) to find the number of hours to fill the pool with the two hoses:

18,000 gal / (100 gal/h) = 180 h

Verify: 100 gal / h * 180 h = 18,000 gal

Answer: 180 hours