9 large pipes drains a pond in 8 hours and 6 small pipes drains a pond in 16 hours How long will 3 large pipes and 5 small pipes take to drain a pond?

Answer 1

If 9 large pipes take 8 hours to drain the pond,

then 1 large pipe would take 8*9=72 hours.

large_pipe_rate = (1/72) pond/hour

Since 6 small pipe drain the pond in 16 hours,

then 1 small pipe would take 6*16 = 96 hours.

small_pipe_rate = (1/96) pond/hour

Now we can calculate using:

rate * time = work done

In this case, we have two rates, but a common time,

so we will have:

(3*large_pipe_rate)*time + (5*small_pipe_rate)*time = 1

Plug in the values we know and solve for "time":

(3*large_pipe_rate)*time + (5*small_pipe_rate)*time = 1

(3 * (1/72))*time + (5 * (1/96))*time = 1

(3/72)*time + (5/96)*time = 1

(3/72 + 5/96)*time = 1

time = 1/(3/72 + 5/96)

time = 1/.09375000

time = 10.66666667

Answer:

3 large pipes and 5 small pipes could drain

the pond in 10 and 2/3 hours (which is

10 hours and 40 minutes).

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The other answers disagree with me. I would like you to

get this problem correct, and to be honest, I'd like the

points for showing the correct way to do it. So, I'll take

a moment to show you why the other answers don't

even make sense.

Consider if all 8 pipes were large. We know that *9*

large pipes could drain the pond in 8 hours. With a

little calculation, we can see that 8 large pipes could

drain it in 9 hours:

8 * (1/72) * time = 1

(1/9) * time = 1

time = 9 hours

If all 8 pipes were small, then it would take:

8 * (1/96) * time = 1

(1/12)* time = 1

time = 12 hours

So we **know** it will be somewhere between 9

and 12 hours. Certainly NOT 16 hours.

Go back to the problem statement and notice that 6

small pipes can drain the pond in 16 hours. The other

answers claim that 5 small pipes + 3 large pipes also

take 16 hours. Therefore, their claim is that:

6 small pipes = 5 small pipes + 3 large pipes

In other words, by removing 1 of the 6 small pipes and

adding 3 large ones, the drain time remains at 16 hours:

1 small pipe = 3 large pipes

Nonsense.

Bottom line:

3 large + 5 small will take 10 hours and 40 minutes.