Water injection in mathematical problems
Sixth grade olympiad math exercise: water injection.
Exercise: A pool is equipped with a normally open drain pipe at the bottom and several water inlet pipes with the same thickness at the top. Four water inlet pipes are opened, and it takes 5 hours to fill the pool; Two water inlet pipes are opened, and it takes 15 hours to fill the pool; It takes two hours to fill the pool now. How many water inlet pipes should be opened at least?
Answer and analysis: Water injection (drainage) is a special kind of engineering problem. Filling or draining a pool is equivalent to a project, and the flow of water is the workload, and the flow of water per unit time is the work efficiency.
The pool needs to be filled within 2 hours, that is, the difference between the water inflow and the water displacement within 2 hours is just a pool of water. Therefore, it is necessary to know the working efficiency and total workload (one pool of water) of the water inlet pipe and the drainage pipe.
As long as one quantity is set to 1, the other two quantities can be deduced from the condition.
Assuming that the hourly water injection quantity of each same water inlet pipe is 1, the five-hour water injection quantity of four water inlet pipes is (1×4×5), and the five-hour water injection quantity of two water inlet pipes is (1× 2× 15), it can be seen that
The hourly displacement is (1× 2×15-1× 4× 5) ÷ (15-5) =1.
In other words, the drain pipe has the same working efficiency as each water inlet pipe. It can be seen that
The total workload of a pool of water is1× 4× 5-1× 5 =15.
Since the water injection amount of each water inlet pipe is 1×2 within 2 hours,
So, fill a pool of water in 2 hours.
How many water inlet pipes do you need at least? (15+1x2) ÷ (1x2) = 8.5 ≈ 9 (pieces)
A: At least 9 water inlet pipes are required.
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