It takes an older pump 4 times as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps 4 hours to drain the pool. How long will it take the older pump to drain the pool working alone?
Let's assume it takes the newer pump x hours to drain the pool alone.
According to the information given, it takes the older pump 4 times as long as the newer pump to drain the pool. So, it takes the older pump 4x hours to drain the pool alone.
When the two pumps work together, they can drain the pool in 4 hours.
So, we can set up an equation based on their combined rates of work:
1/x + 1/4x = 1/4
To solve this equation, we can multiply both sides by 4x to get rid of the fractions:
4 + 1 = x
Simplifying further, we have:
5 = x
Therefore, it takes the newer pump 5 hours to drain the pool alone.
Since the older pump takes 4 times as long, it will take the older pump 4 * 5 hours = 20 hours to drain the pool alone.
So, it will take the older pump 20 hours to drain the pool working alone.
To solve this problem, let's assign variables to represent the time it takes each pump to drain the pool. Let's use 'N' for the time taken by the newer pump and 'O' for the time taken by the older pump.
Given that it takes the older pump 4 times as long as the newer pump to drain the pool, we can set up the equation:
O = 4N (Equation 1)
We are also given that when the two pumps work together, they can drain the pool in 4 hours:
1/N + 1/O = 1/4 (Equation 2)
Now we have a system of two equations (Equations 1 and 2) that we can solve simultaneously.
Let's substitute the value of O from Equation 1 into Equation 2:
1/N + 1/(4N) = 1/4
To simplify the equation, we can multiply all terms by the least common denominator (LCD), which is 4N:
4 + 1 = N
N = 5
Now that we have found the time taken by the newer pump, we can substitute this value into Equation 1 to find the time taken by the older pump:
O = 4N
O = 4 * 5
O = 20
Therefore, the older pump will take 20 hours to drain the pool working alone.
If the fast pump takes x hours, then
1/x + 1/(4x) = 1/4
Solve for x, and then use 4x as your time.