Fixing a Partial Tank with One Tap: A Practical Approach
Understanding the Problem
As we delve into solving the practical problem of filling a tank with taps, we'll examine a scenario where two identical taps fill a fraction of the tank in a given time. This article will guide you through a detailed analysis and solution using the principles of filling rate and efficiency.Finding the Filling Rate of Both Taps
Imagine a tank that is partially filled. Let's start by determining the rate at which the taps fill the tank. Given that two identical taps fill (frac{2}{5}) of the tank in 20 minutes, we can begin by calculating the combined filling rate of both taps.Combined Filling Rate:
[ text{Combined Filling Rate} frac{frac{2}{5} text{ tank}}{20 text{ minutes}} frac{2}{100} frac{1}{50} text{ tank per minute} ] This shows that both taps working together can fill (frac{1}{50}) of the tank per minute.Calculating the Filling Rate of One Tap
Since the taps are identical, we can determine the rate of one tap by halving the combined rate.Filling Rate of One Tap:
[ text{Filling Rate of One Tap} frac{1}{2} times frac{1}{50} frac{1}{100} text{ tank per minute} ] Therefore, one tap alone can fill (frac{1}{100}) of the tank per minute.Calculating the Time Required to Fill the Remaining Tank
Now, let's calculate the time required for the remaining one tap to fill the rest of the tank. Initially, (frac{2}{5}) of the tank is filled, so the remaining part of the tank to be filled is (frac{3}{5}).Time for One Tap to Fill the Remaining Tank:
[ text{Time} frac{text{Remaining Tank}}{text{Filling Rate of One Tap}} frac{frac{3}{5}}{frac{1}{100}} frac{3}{5} times 100 60 text{ minutes} ] Thus, the remaining tap needs 60 minutes to fill the rest of the tank.