The time taken, t minutes, to fill up a bottle is inversely proportional to the rate of waterflow, v mℓ/min. It takes 5 minutes to fill up the bottle when the rate of waterflow is 500 mℓ/min. Find the time taken to fill up the bottle when the rate of the waterflow is 625 mℓ/min.
Question
The time taken, t minutes, to fill up a bottle is inversely proportional to the rate of waterflow, v mℓ/min. It takes 5 minutes to fill up the bottle when the rate of waterflow is 500 mℓ/min. Find the time taken to fill up the bottle when the rate of the waterflow is 625 mℓ/min.
Solution
Given that the time taken to fill up the bottle is inversely proportional to the rate of water flow, we can express this relationship mathematically as:
t = k/v
where: t is the time taken to fill up the bottle, v is the rate of water flow, and k is the constant of proportionality.
From the problem, we know that it takes 5 minutes to fill up the bottle when the rate of water flow is 500 ml/min. We can use this information to find the constant of proportionality, k.
5 = k/500
Solving for k gives us:
k = 5 * 500 = 2500
Now that we have the constant of proportionality, we can find the time taken to fill up the bottle when the rate of water flow is 625 ml/min.
t = 2500/625 = 4 minutes
So, it would take 4 minutes to fill up the bottle when the rate of water flow is 625 ml/min.
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