Question

oil flows back and forth between a small and large tank. when oil is moving into the large tank, the flow rate is positive. when oil is moving into the small tank, the flow rate is negative. the large tank begins with 600 gallons of oil. the flow rate is recorded as -4 gallons per minute. after a period of 32 minutes, how much oil has been moved and to which tank? \\(\boldsymbol{\downarrow}\\) into the \\(\boldsymbol{\downarrow}\\) tank. after the 32 minutes, how much oil is in the large tank? \\(\boldsymbol{\downarrow}\\) gallons

Explanation:

Step1: Determine the amount of oil moved

The flow rate is -4 gallons per minute (negative means moving into the small tank, so out of the large tank). Time is 32 minutes. To find the amount of oil moved, we use the formula: Amount = Rate × Time. So, the amount of oil moved is $-4 \times 32 = -128$ gallons. The negative sign indicates it's moved out of the large tank (into the small tank). The absolute value of -128 is 128, so 128 gallons of oil have been moved into the small tank.

Step2: Calculate the oil in the large tank after 32 minutes

The large tank initially has 600 gallons. We subtract the amount of oil moved out (128 gallons) from the initial amount. So, the amount of oil in the large tank is $600 - 128 = 472$ gallons.

Answer:

• How much oil has been moved and to which tank? 128 gallons into the small tank.
• After 32 minutes, how much oil is in the large tank? 472 gallons.