it takes 3 hours for ten pumps to pump 40000l of water ino a dam. how long will it take nine pumps to pump 60000l of water into a dam
40000 L takes 30 pump-hr
so 60000 L takes 45 pump-hr
... one and a half times as much
45 pump-hr / 9 pump = ?
9/10 the pumps, 10/9 the time.
3/2 the volume, 3/2 the time.
10/9 * 3/2 = 5/3 the time.
5/3 * 3 = 5 hours
To find out how long it will take nine pumps to pump 60000 liters of water into a dam, we can use the concept of "work."
We know that:
- 10 pumps took 3 hours to pump 40000 liters of water.
First, let's calculate the work done by 10 pumps in 1 hour:
Work done by 10 pumps in 1 hour = 40000 liters / 3 hours = 13333.33 liters/hour
Next, we can use the concept of "work rate" to find out how long it will take 9 pumps to pump 60000 liters of water:
Work rate of 10 pumps = 13333.33 liters/hour
Work rate of 9 pumps = (9/10) * 13333.33 liters/hour = 11999.99 liters/hour
Now, let's calculate the time it will take for 9 pumps to pump 60000 liters of water:
Time = Work / Work rate = 60000 liters / 11999.99 liters/hour
Using a calculator, we can find:
Time = 5 hours
Therefore, it will take nine pumps 5 hours to pump 60000 liters of water into the dam.
To determine how long it will take nine pumps to pump 60000 liters of water into the dam, we can use the concept of pump efficiency.
The efficiency of the pumps can be calculated as:
Efficiency = Output / Time
where Output is the amount of water pumped and Time is the duration it takes to pump that amount of water.
In this case, we know that with ten pumps, it takes 3 hours to pump 40000 liters of water. So, for ten pumps:
Efficiency = 40000 liters / 3 hours
To find out how long it will take nine pumps to pump 60000 liters of water, we need to calculate the efficiency of nine pumps and then rearrange the equation to solve for time.
Efficiency of nine pumps = 60000 liters / Time (unknown)
Now, let's set up an equation to find the time it will take for nine pumps:
Efficiency (10 pumps) = Efficiency (9 pumps)
40000 liters / 3 hours = 60000 liters / Time
To solve for Time, we can cross-multiply and then divide:
40000 liters * Time = 60000 liters * 3 hours
Now, let's do the math:
40000 * Time = 60000 * 3
Divide both sides by 40000 to isolate Time:
Time = (60000 * 3) / 40000
Calculating further:
Time = 180000 / 40000
Time = 4.5
Therefore, it will take nine pumps 4.5 hours to pump 60000 liters of water into the dam.