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Picture two pipes, A and B, on a mission to fill a tank. Pipe A needs 15 minutes, and Pipe B needs 20. They kick off together, but after 4 minutes, Pipe A takes a break. Want to know how much more time is needed to fill the tank completely? Let’s figure it out!
Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, Pipe A is turned off. What is the total time required to fill the tank?
It will take 14 minutes and 40 seconds to fill the tank.
Explanation
Calculate the work rate of each pipe:
- Pipe A: 1 tank / 15 minutes = 1/15 tank/minute
- Pipe B: 1 tank / 20 minutes = 1/20 tank/minute
Calculate the work done in 4 minutes:
- Work done = (work rate of A + work rate of B) * time
- Work done = (1/15 + 1/20) * 4 minutes
- Work done = 4/60 tank
Calculate the remaining work:
- Remaining work = 1 tank – work done in 4 minutes
- Remaining work = 1 tank – 4/60 tank
- Remaining work = 8/15 tank
Calculate the time taken by pipe B to finish the remaining work:
- Time taken = remaining work / work rate of B
- Time taken = 8/15 * 20 minutes
- Time taken = 10 2/3 minutes
Add the time taken in both stages to find the total time:
- Total time = time taken in 4 minutes + time taken by pipe B
- Total time = 4 minutes + 10 2/3 minutes
- Total time = 14 2/3 minutes
Therefore, it takes 14 minutes and 40 seconds to fill the tank.
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Ratio and Proportion
Ratio and proportion are mathematical concepts that deal with the relationship between two or more quantities. They are often used in various real-life situations to compare and scale quantities.
Ratio: A ratio is a way of expressing the relationship between two quantities. It is typically written as a fraction or using the colon symbol. For example, if there are 3 red balls and 5 blue balls, the ratio of red to blue balls is 3:5 or 3/5. Ratios can be simplified, and they can also be multiplied or divided by the same non-zero number without changing the relationship.
Proportion: A proportion is an equation that states that two ratios are equal. In other words, if a/b = c/d, then a and d are in proportion to b and c. Proportions are commonly used to solve problems involving unknown quantities.
Example: Suppose you have a recipe that requires 2 cups of flour and 3 cups of sugar to make a certain dessert. The ratio of flour to sugar is 2:3. If you want to make more of the dessert and need to know how much sugar is required when using 4 cups of flour, you can set up a proportion:
2/3 = 4/x
Now, cross-multiply to solve for x:
2x = 12
Divide by 2:
x = 6
So, when using 4 cups of flour, you would need 6 cups of sugar to maintain the same ratio.
These concepts are used in a variety of fields, such as mathematics, physics, engineering, and everyday situations like cooking, where precise measurements and scaling are important.
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Source: Math Hello Kitty
Categories: Math
