Variation can be direct, inverse and joint. It will take 2 hours to empty the tank at a rate of 500 gallons per minutes Let time be represented with t, and r represent rate. The inverse variation is represented as: Represent as an equation Make k the subject When t = 2.5 and r = 400, we have: When r = 500, we have: Divide both sides by 500 : Hence, it will take 2 hours to empty the tank at a rate of 500 gallons per minutes
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The equation for inverse variation is: rt = k
To find the value of k, we plug in the values of t and r when the tank is emptied in 2 hours at a rate of 500 gallons per minute:
2 * 500 = k
k = 1000
So, the equation for this scenario is rt = 1000
When t = 2.5 and r = 400, we have:
(2.5) * 400 = 1000
When r = 500, we have:
t * 500 = 1000
t = 1000 / 500
t = 2 hours
Therefore, it will take 2 hours to empty the tank at a rate of 500 gallons per minute.