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Pani-rosa [81]
3 years ago
14

2 taps A and B can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 5 hours less than tap B to fill the same

pool. How many hours does it take tap A to fill the pool?
Mathematics
1 answer:
vazorg [7]3 years ago
4 0

Answer:

Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.

Step-by-step explanation:

Let tap B fills the pool alone in the time = x hours

So in one hour part of pool will be filled = \frac{1}{x}

Another tap A when turned on, it takes time to fill the pool = x-5 hours

So in one hour part of the same pool filled = \frac{1}{x-5}

Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.

Part of the pool filled in one hour by both the taps = \frac{1}{3}

Now we form an equation

Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on

\frac{1}{(x-5)}+\frac{1}{x}=\frac{1}{3}

\frac{x-5+1}{x(x-5)}=\frac{1}{3}

\frac{x-4}{x(x-5)}=\frac{1}{3}

3(x - 4) = x(x - 5)

x² -5x = 3x - 12

x² - 8x + 12 = 0

x² - 6x - 2x + 12 = 0

x(x - 6) - 2(x - 6) = 0

(x -2)(x - 6) = 0

x = 2, 6 hours

We will take higher value of x as x = 6 hours for tap B.

Time taken by tap A = 6 - 4 = 2 hours.

Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.

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First, let's check if the sequence is geometric or arithmetric.

If arithmetric, the sequence will have common difference.

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<u>G</u><u>e</u><u>o</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u>

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To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.

Let's check by dividing sequences.

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Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.

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Because the common ratio is -3. Let these be the following:

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From the:

\displaystyle \large{ \frac{a_{n + 1}}{a_n}  = r}

Substitute the values in.

\displaystyle \large{ \frac{y}{2}  =  - 3}

Multiply the whole equation by 2 to isolate y.

\displaystyle \large{ \frac{y}{2} \times 2  =  - 3 \times 2} \\  \displaystyle \large{ y =  - 6}

Therefore, the value of y is -6.

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