Tap A fills a tube with cold water in 6 minutes. Tap B fills a tube with hot water in 8 minutes. If water is flowing out from taps A and B at the same time, how long does it take to fill the tubes?
A's rate = 1/6
B's rate = 1/8
combined rate = 1/6 + 1/8 = 7/24
time to fill with combined rate = 1/(7/24) = 24/7 minutes
To solve this problem, you'll need to calculate the rate at which the taps fill the tubes and then determine how long it will take for the combined flow from taps A and B to fill the tubes.
Let's start by determining the rates at which taps A and B fill their respective tubes.
Tap A fills a tube with cold water in 6 minutes. This means that in 1 minute, the tap fills 1/6th of the tube. Therefore, the rate of tap A is 1/6 tube per minute.
Similarly, Tap B fills a tube with hot water in 8 minutes. In 1 minute, the tap fills 1/8th of the tube. Therefore, the rate of tap B is 1/8 tube per minute.
To find the combined rate of taps A and B when they are flowing simultaneously, we simply add their individual rates together. So, the combined rate is 1/6 + 1/8 tube per minute, which can be simplified to 7/24 tube per minute.
Now, to determine the time it takes to fill the tubes when both taps are flowing, we can use the formula:
Time = Volume / Rate
Since we want to find the time, let's assume the volume of the tube is 1 unit.
Time = 1 / (7/24) = 24/7 minutes
Therefore, it will take approximately 3.43 minutes (or 3 minutes and 26 seconds) to fill the tubes when both taps A and B are flowing.