# How much time will be required by 1 single large pipe to fill the pool in the following case? Four small pipes can fill a swimming pool in 16 minutes. If four larger pipes are used too, the time...

How much time will be required by 1 single large pipe to fill the pool in the following case?

Four small pipes can fill a swimming pool in 16 minutes. If four larger pipes are used too, the time taken is 4 minutes.

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There are 4 pipes to fill a swimming pool in 16 min.

==> 1 small pipe will fill the pool in 16*4 = 64 min.

==> after 4 minutes

1 pool = 64 min

v = 1 min.

==> v = 1/64 ( the portion of the pool filled with 1 small pipe in one minute)

==> v= 4/64 = 1/16 ( the potion will be filled with 4 small pipes in 1 min)

==> 1/4 the pool will be filled in 4 minutes with 4 small pipes.

==> 3/4 the pool will be filled with 4 larger pipes in 4 minutes.

==> (3/4)/4 = 3/16 will be filled with 4 larger pipes in 1 minutes.

==> (3/16)/4 will be filled with 1 large pipe in 1 minute.

==> 3/64 of the pool will be filled with 1 large pipe in 1 minute.

==> To fill the pool we will need 64/3*3/64 = 1 v

==> we will need 64/3 minutes.

**==> 21.3 minutes required to fill the pool with one large pipe.**

I take that all the small pipes and all the large pipes fill at the same rate. Now 4 small pipes fill the pool in 16 minutes, so 1 small pipe will take 16*4 = 64 minutes to fill the pool.

When 4 large pipes are used too, all the pipes together take 4 minutes to fill the pool. So we can say that 1 small pipe and 1 large pipe take 4*4 = 16 minutes to fill the pool.

Now, we already know that it takes 64 minutes to fill the pool with a small pipe. So the pipe fills at the rate of 1/64 of the pool per minute. A large pipe and a small pipe together fill at the rate of 1/16 of the pool per minute. So one large pipe alone will fill at the rate of (1/16) – (1/64) = 3/ 64 of the pool per minute.

**Therefore it will take 64/3 = 21.333 minutes to fill the pool with a single large pipe.**