At a factory workers are draining a large vat containing water. The water is being drained at a constant rate. The table below shows the amount of water in the vat after different amounts of time.Time (minutes) 15 20 25 30Water (liters) 620 560 500 440Answer the following questions.(a)Choose the statement that best describes how the time and the amount of water in the vat are related. Then give the value requested.As time increases, the amount of water in the vat decreases.At what rate is the amount of water in the vat decreasing?litersperminuteAs time increases, the amount of water in the vat increases.At what rate is the amount of water in the vat increasing?litersperminute(b)How much water was in the vat when the workers started draining it?liters
Question
At a factory workers are draining a large vat containing water. The water is being drained at a constant rate. The table below shows the amount of water in the vat after different amounts of time.Time (minutes) 15 20 25 30Water (liters) 620 560 500 440Answer the following questions.(a)Choose the statement that best describes how the time and the amount of water in the vat are related. Then give the value requested.As time increases, the amount of water in the vat decreases.At what rate is the amount of water in the vat decreasing?litersperminuteAs time increases, the amount of water in the vat increases.At what rate is the amount of water in the vat increasing?litersperminute(b)How much water was in the vat when the workers started draining it?liters
Solution
(a) The statement that best describes how the time and the amount of water in the vat are related is: As time increases, the amount of water in the vat decreases.
To find the rate at which the water is decreasing, we can subtract the amount of water at two different times and divide by the difference in time. For example, at 30 minutes there are 440 liters and at 15 minutes there are 620 liters. So, the rate is (620-440) / (30-15) = 180 / 15 = 12 liters per minute.
(b) To find out how much water was in the vat when the workers started draining it, we need to add the amount of water drained in the first 15 minutes to the amount of water at 15 minutes. Since the water is being drained at a rate of 12 liters per minute, in 15 minutes, 12 * 15 = 180 liters of water was drained. So, the initial amount of water was 620 + 180 = 800 liters.
Similar Questions
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