time it takes pipes to drain a pond

Question

Nine large pipes will drain a pond in eight hours and six small pipes will drain the same pond in sixteen hours.  How long will it take 3 large pipes and 5 small pipes to drain the pond?

Answer 1

One large pipe takes 9*8 = 72 hours to drain the swamp (proportion and inverse variation)

 

Hence in one hour one large pipe drains 1/72 of the pond  (rate of draining = size of swamp/time)

 

One small pipe takes 6*16 = 96 hours to drain the swamp

 

Hence in one hour one small pipe drains 1/96 of the pond

 

Therefore 3 large and 5 small pipes in one hour will drain; 3*1/72 + 5*1/96 = 1/24 + 5/96 = 9/96 of the swamp

 

therefore it takes 96/9 hours for 3 large and 5 small pipes to drain the swamp = 10.67 hours

Answer 2

We will calculate what part of the pond 1 pipe will drain.

1. Large pipe

9 pipes will drain in 8 hours

then,

1 pipe for 1 hour will drain 1/(9p•8ho) = 1/72 part of pond.

 

2. Small pipe

6 pipes will drain in 16 ho

1 pipe for 1 hour will drain 1/(6p•16ho)=1/96 part of pond.

 

We need t (for time) hours to drain 1 pond.

3 big pipes and 5 small pipes for 1 hour will drain

3(1/72)      +     5(1/96)           part.

We need t hours for 1 pond.

We multiply the above part and hours to get 1.

[3/72 +5/95]t=1

9/96 t =1

t = 1/[9/96]

t =96/9 hours

t = 10 and 2/3 hours or

      10 hours 40 min.

 

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