Submitted by Anonymous (not verified) on
Forums:
Sup peeps,
At school, a teacher gave us this riddle and we had to solve it. It was interesting so I thught I'd share it with you guys:
A + B = 3 hours
A + C = 4 hours
B + C = 5 hours
How long will it take for Pump A, B & C to clear the water?
Good luck peeps!
Pump Efficiency Question
Submitted by Jack K. (not verified) on
Do you know the answer? I got 2.55 hrs, or 2 hours 33 mins and 11.5 seconds. Is this right?
If it is, I can post my working.
Yep I do
Submitted by Username (not verified) on
The answer is 2.5454... hours according to all my teachers yet when I worked it out I got 2.4545... hours. However, since you got the same answer as my teachers, mind showing me how you did it? First I worked out the ratios: A:B:C, 1:2:3. So A is twice as powerful as B and A is three times as powerful as C. Then I made B in terms of A: B = A/2 (Talking about the power here). Then I subsituted it into the first equation: A + B = 3 hours, so to work out how much water, (A + A/2)*3 = Total water. Then I got 9A/2 as the total water. Next I started adding the pump effiecencies: A + A/2 + A/3 which is 11A/6. And finally I did the total water divided by the pump power which is (9A/2) / (11A/6) which is (27/11)... which in decimals is 2.454545 hours.
I think I done something wrong, I can sense it, it's probably the calculating of pump powers.
Anyways, you got it right btw :)
My method
Submitted by Jack K. (not verified) on
I took an entirely different route, calling the efficiency of pump A "a litres per hour", of B "b litres per hour", and of C "a litres per hour". Then I worked out how much of the water each combination clears in 1 hour:
1. a+b = 1/3 (because in 3 hours all the water is gone, so in 1 hour 1/3 of the water is cleared)
2. a+c = 1/4
3. b+c = 1/5
Then subtracting equation 2 from equation 3 gets:
4. a-b = 1/20
Adding 4 to 1 gets
2a = 23/60
5. a = 23/120
From her I worked out b = 17/120 and c = 7/120. So altogether in one hour they clear
6. a+b+c = 47/120 of the tank
So to clear the whole tank they need 120/47 hours or 2.553191489... hours. Looks like I got a slightly different answers to both you and your teachers! :)
I don't understand in your solution how you got that the ratio A:B:C of the powers was 1:1/2:1/3?
Same
Submitted by Leipzig (not verified) on
That's the answer I got, although I used a much lazier and less elegant solution
Same again
Submitted by Darth Complex (not verified) on
Yeah, I did it pretty much the same way and got exactly the same answer
Nearly there
Submitted by Username (not verified) on
Your solution looks legit to be honest but I'll post my teachers solution in full once I get it. Yeah and mine was wrong.
UPDATE
Submitted by Username (not verified) on
Sorry peeps if you're waiting for the answer, I'll post it tomorrow around 5pm.