Question 1191661: Hi
A pool 100cm by 100cm by 435cm is to be filled to the brim. Water from A and B flows at the rate of 150 litres per minute and 250 litres per minute respectively. If A was turned on 3 minutes after B is turned on how long will it take to fill the pool.
Thanks
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = duration (in minutes) that hose B is running
x-3 = duration (in minutes) that hose A is running
This is because hose B had a 3 minute head start, so it runs for 3 minutes longer.
Based on that and the given speeds, we can say,
A = 150(x-3) = 150x-450 = amount of water hose A contributes
B = 250x = amount of water hose B contributes
Amounts are in liters.
A+B = (150x-450)+250x = 400x-450 = total amount of water from both hoses after x minutes elapse.
At this point, we need to find out how much water will fill the pool. We'll need the volume of the pool.
Assuming the pool is a rectangular prism, then,
Volume = (length)*(width)*(height)
V = L*W*H
V = (100 cm)*(100 cm)*(435 cm)
V = (100*100*435)*(cm*cm*cm)
V = 4,350,000 cm^3
Think of tiny 1 cm by 1 cm by 1 cm blocks.
We'll need 4,350,000 of them (a little over 4.3 million) to fill the pool if we stack and pack the blocks in perfectly.
Side note: cm^3 = cubic centimeter = cubic cm = cc
By definition, 1 cm^3 is equal to 1 mL
The pool has a volume of 4,350,000 mL
To convert to liters, we divide by 1000 since 1000 mL = 1 liter
So,
(4,350,000)/1000 = 4,350
Just chop off the last 3 zeros of "4,350,000" to arrive at 4,350
The pool has a volume of 4,350 liters.
Set this equal to the A+B expression mentioned earlier and solve for x.
400x-450 = 4350
400x = 4350+450
400x = 4800
x = 4800/400
x = 12
It will take 12 minutes from the time hose B (ie the first hose) is activated, to completely fill the pool with both hoses based on the conditions stated in the instructions.
Since hose B contributes water at a rate of 250 liters/min, and does so for 12 minutes, it contributes 250*12 = 3000 liters of water.
Hose A starts 3 minutes later and has a duration of x-3 = 12-3 = 9 minutes. It contributes 150*9 = 1350 liters.
The two hoses combine to give A+B = 1350+3000 = 4350 liters which is the volume of the pool (again assuming it is a rectangular prism).
Another assumption is that none of the water spills out of the pool, and evaporation shouldn't be that big an issue.
Answer: 12 minutes
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