The time taken, t minutes, to fill up a bottle is inversely proportional to the rate of waterflow, v mℓ/min. When the rate of waterflow is 950 mℓ/min, the time taken to fill up the bottle is 12 minutes. If the rate of the waterflow is 760 mℓ/min, find the time taken to fill up the bottle.
Question
The time taken, t minutes, to fill up a bottle is inversely proportional to the rate of waterflow, v mℓ/min. When the rate of waterflow is 950 mℓ/min, the time taken to fill up the bottle is 12 minutes. If the rate of the waterflow is 760 mℓ/min, find the time taken to fill up the bottle.
Solution
Given that the time taken, t minutes, to fill up a bottle is inversely proportional to the rate of waterflow, v mℓ/min, we can express this relationship mathematically as:
t = k/v
where k is the constant of variation.
We know that when v = 950 mℓ/min, t = 12 minutes. We can substitute these values into the equation to find the constant of variation:
12 = k/950
Solving for k gives us:
k = 12 * 950 = 11400
Now we know the constant of variation, we can find the time taken to fill up the bottle when the rate of waterflow is 760 mℓ/min. Substituting these values into the equation gives us:
t = 11400/760 = 15 minutes
So, when the rate of waterflow is 760 mℓ/min, it takes 15 minutes to fill up the bottle.
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