3 PUMPS WORKING 8 HOURS A DAY, CAN EMPTY A TANK IN 2 DAYS. HOW MANY HOURS A DAY MUST 4 PUMPS WORK TO EMPTY THE TANK IN 1 DAY?
The three pumps work 3*8*2=48 hrs in 2 days, so one pump can empty 1/48 of the tank in an hour.
4 pumps can empty 4/48 = 1/12 of the tank in one hour.
so, . . .
10
To find out how many hours a day 4 pumps must work to empty the tank in 1 day, we can use the following logic:
Let's assume that each pump works at a constant rate.
We know that 3 pumps working for 8 hours a day can empty the tank in 2 days.
So, the total work done by 3 pumps in 2 days is equal to the work required to empty the tank.
Let's assign a variable to the total work required to empty the tank.
Let x be the work required to empty the tank.
Now, we can create a proportion to solve for x:
3 pumps * 8 hours/day * 2 days = 4 pumps * y hours/day * 1 day
Simplifying this proportion, we get:
48 = 4y
Divide both sides by 4:
y = 48/4
y = 12
Therefore, 4 pumps must work for 12 hours a day to empty the tank in 1 day.
To solve this problem, we can use the concept of work rates.
Let's start by finding the work rate of each pump. Since we know that 3 pumps can empty the tank in 2 days, we can say that the work rate of each pump is 1/6th of the tank per day.
Now, let's find the total work rate when 3 pumps are working together. We can simply add up their individual work rates:
Total work rate of 3 pumps = (1/6) + (1/6) + (1/6) = 1/2 of the tank per day.
Now, we need to find out how many hours 4 pumps need to work to empty the tank in 1 day. We can assume that each pump works at the same rate as before, so the work rate of each pump is still 1/6th of the tank per day.
Since we want to empty the tank in 1 day, we need to find the work rate required for 4 pumps. Let's call it R.
Work rate * Time = Work
(R * 1 day) = 1 tank
Now, we know that the total work rate of 3 pumps is 1/2 tank per day, so the work rate of 4 pumps would be 4/3 times the work rate of 3 pumps.
(R * 1 day) = (4/3 * 1/2 tank)
R = 4/6
R = 2/3
Hence, the work rate of 4 pumps is 2/3 tank per day.
Since we want to find how many hours a day 4 pumps must work, we can divide the work rate by the number of pumps working and then multiply by 24 hours.
Work rate per pump = (2/3) / 4 = 1/6 tank per day
Hours per day = (1/6 tank per day) * 24 hours = 4 hours
Therefore, 4 pumps must work 4 hours per day to empty the tank in 1 day.