Imagine you have a tank that needs to be filled with water. Sounds simple enough, right? Wrong! It gets a little more complicated when you factor in two pipes, A and B. Pipe A can fill the tank in 15 minutes, while pipe B can do it in 20. But what happens when you open both pipes at the same time, and then turn off pipe A after 4 minutes? How long will it take to fill the entire tank? Get ready to solve the great tank filling conundrum!
First, let's break down what we know. Pipe A can fill the tank in 15 minutes, which means it can fill 1/15th of the tank in just one minute. Pipe B, on the other hand, can fill 1/20th of the tank in one minute. Now let's say we open both pipes at the same time. That means we're filling the tank at a rate of 1/15 + 1/20, or 7/60th of the tank per minute.
Now, after 4 minutes, we turn off pipe A. This means that for the remainder of the time, we're only using pipe B, which can fill 1/20th of the tank per minute. So how long will it take to fill the remaining amount? Well, we know that after the first 4 minutes, we've already filled up 4*(7/60)th of the tank, or 7/15ths of it. That means we still have 8/15ths left to fill.
If pipe B can fill 1/20th of the tank per minute, then it will take 8/15 ÷ (1/20) minutes to fill the remaining amount. Simplifying the equation, we get (8/15) * (20/1), which equals 32/3 minutes, or 10 minutes and 40 seconds.
So, to answer the question that started it all – how long does it take to fill the entire tank when using both pipes A and B for the first four minutes, and then only pipe B for the rest? It will take a total of 4 minutes + 10 minutes and 40 seconds, or 14 minutes and 40 seconds.
In conclusion, solving the puzzle of two pipes A and B might seem complicated at first glance, but with the power of math, we can figure it out. Just remember to think about how much of the tank each pipe can fill, and how much time is spent using each one. Who knew filling a tank with water could be so mathematically intriguing?
