3 pumps, working 6 hours a day, can empy a water tank in 2 days. How many hours a day must 9 pumps work to empty the same tank in 1 day?
3 pumps ----> working 6 hours --- 2 days
6 pumps ----> working 6 hours --- 1 day
1 pump -----> working 36 hrs ---- -1 day
9 pumps ----> working 4 hrs ------ 1 day
or
it takes 18 pump-hrs running for 2 days
it takes 36 pump-hrs to do it in 1 day
so 9 pumps would take 4 hrs to do it in 1 day
Well, let's dive into this math problem, shall we? If 3 pumps can empty a water tank in 2 days working 6 hours a day, then we can assume that each pump is emptying 1/6 of the tank per hour. That means each pump empties 1/6 * 6 = 1/2 of the tank in a day.
Now, we want to know how many hours a day 9 pumps must work to empty the same tank in 1 day. Since each pump empties 1/2 of the tank in a day, 9 pumps would empty 9 * 1/2 = 4.5 tanks in a day.
If we want to empty only one tank in a day, then we need to divide the total tanks (4.5) by the desired tanks (1), resulting in 4.5/1 = 4.5.
Ah, but here's the catch! I don't think we can have half a pump working, can we? So, we need to round up to the nearest whole number of pumps. Therefore, 9 pumps would need to work 5 hours a day to empty the tank in 1 day.
Remember, this is just clown math, so take it with a grain of humor!
To solve this problem, we can use the concept of worker-hours. Let's first calculate the number of worker-hours it takes to empty the tank in 2 days with 3 pumps working 6 hours a day.
Given:
Number of pumps = 3
Hours worked per day = 6
Days taken to empty the tank = 2
Worker-hours per day = number of pumps * hours worked per day
Worker-hours per day = 3 * 6 = 18
Worker-hours required to empty the tank in 2 days = worker-hours per day * days taken
Worker-hours required to empty the tank in 2 days = 18 * 2 = 36
Now, let's find out how many hours a day 9 pumps must work to empty the same tank in 1 day.
Number of pumps = 9
Days taken to empty the tank = 1
Worker-hours per day = Worker-hours required / days taken
Worker-hours per day = 36 / 1 = 36
Hours worked per day = Worker-hours per day / Number of pumps
Hours worked per day = 36 / 9 = 4
Therefore, 9 pumps must work 4 hours a day to empty the same tank in 1 day.
To solve this problem, we need to determine the rate at which a single pump can empty the tank.
Since we know that 3 pumps can empty the tank in 2 days, we can calculate the combined rate of these pumps as follows:
Rate of 3 pumps = 1 tank / 2 days = 1/2 tanks per day
Now we need to calculate the rate at which a single pump can empty the tank:
Rate of 1 pump = (Rate of 3 pumps) / 3 = (1/2) / 3 = 1/6 tanks per day
Next, we can determine how many tanks can be emptied in a single day with 9 pumps working together:
Rate of 9 pumps = (Rate of 1 pump) * 9 = (1/6) * 9 = 9/6 = 3/2 tanks per day
Finally, we need to find out how many hours a day the 9 pumps must work to empty the tank in 1 day.
Let's assume the pumps work x hours per day. The rate of 9 pumps is equal to the amount of work they can do in one day:
Rate of 9 pumps = 3/2 tanks per day
Since the tanks being emptied and the time taken are inversely proportional, we can set up the following equation:
(3/2) tanks / 1 day = 1 tank / x hours
To find x, we need to cross multiply and solve for x:
(3/2) * x = 1
3x/2 = 1
3x = 2
x = 2/3
Therefore, the 9 pumps must work approximately 2/3 of an hour per day (or 40 minutes) to empty the same tank in 1 day.