How long will it take 3 large pipes and 5 small pipes to drain the pond?Nine large pipes will drain the pond in 8 hours and 6 small pipes will drain it in 16 hours.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is given that nine large pipes take 8 hours to drain the pond and 6 small pipes take 16h.

So 1 large pipe will drain the pond in 8*9= 72 hours or in an hour 1/72 of the pond is drained. And 1 small pipe will take 16*6 = 96 hours to drain the pond or in one hour 1/ 96 of the pond is drained.

3 large pipes and 5 small pipes can drain 3* (1/72) + 5*(1/96) of the pond every hour. So they drain 3/32 of the pond every hour. The complete pond can be drained in 1/(3/32) = 32/3 hours.

The time required by 3 large and 5 small pipes to drain the pond is 32/3 hours.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

 Let Pl = volume drained by one large pipe in one hour

 Let Ps = volume drained by one small pipe in one hour

 Let t = time

   V - 9P*8 = 0                             V-6*p*(16) = 0

  +(-V+6p*16 = 0)                         V = 6*p*16

 -9Pl*8+6ps*16 = 0

   9P*8 = 6p*16                    V-3(P)(t)-5(p)(t) = 0

      P = 1.33p   -------------->  6p*16-3(1.33p)(t)-5(p)(t) = 0

                                               96p-4pt-5pt = 0

                                                96p = 9pt

                                                 t = (96p)/(9p)

                                               t = 10.667 hrs = 10 hrs 40 min

==> t= 10 hrs 40 min

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