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lisov135 [29]
3 years ago
10

A swimming pool is being filled at the rate of 12 cubic yards per minute. If the pool is 18 yards long, 10 yards wide, and 3 yar

ds deep, how many minutes will it take to fill the pool?
Mathematics
2 answers:
horsena [70]3 years ago
7 0
(18*10*3yd^3)(min/12yd^3)

540yd^3(min/12yd^3)=45 minutes
NISA [10]3 years ago
4 0

Answer:

The time taken to fill the pool is 45 minutes.

Step-by-step explanation:

Given : A swimming pool is being filled at the rate of 12 cubic yards per minute. If the pool is 18 yards long, 10 yards wide, and 3 yards deep.

To find : How many minutes will it take to fill the pool?

Solution :

First we find the volume of the swimming pool.

Dimension of pool,

Length = 18 yards

Wide = 10 yards

Depth = 3 yards

The volume of the pool is

V=l\times w\times h

V=18\times 10\times 3

V=540

The volume of the swimming pool is 540 yard cube.

The rate of filling the pool is r=12 cubic yards per minute.

We know, Time taken is

Time=\frac{Volume}{rate}

Time=\frac{540}{12}

Time=45

Therefore, The time taken to fill the pool is 45 minutes.

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Answers:

  • (a) 73440
  • (b)  3060

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

  • 18 choices for slot A
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We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

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in this case n = 18 and r = 4. The exclamation marks indicate factorial.

-----------------------------------

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

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You could use the nCr combination formula to get the same result

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where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

_nC_r = \frac{_nP_r}{r!}

which can be rearranged into

_nP_r = r!*\left( _nC_r \right)

these formulas are handy to help us go back and forth between nCr or nPr.

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