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daser333 [38]
3 years ago
12

Tap A takes 6 minutes to fill a tank and tap b takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. H

ow long will it take to fill the tank if the pipe is in use when both taps are turned on
Mathematics
2 answers:
gavmur [86]3 years ago
8 0

Answer:

x=\frac{90}{19} = 4.73 minutes

\frac{1}{6}x +\frac{1}{9}x - \frac{1}{15} x = 1

\frac{135}{810}x +\frac{90 }{810}x - \frac{54}{810} x = 1

\frac{171}{810}x   = 1

x = 4.73 minutes

Step-by-step explanation:

jekas [21]3 years ago
6 0

Answer:  approximately 4.7368 minutes

This decimal value is the result of computing 90/19

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

Explanation:

Let's find the LCM of 6, 9 and 15. First, list out the prime factorization of each value.

  • 6 = 2*3
  • 9 = 3*3
  • 15 = 3*5

The unique prime factors are 2, 3, and 5. We have 2 show up at most once, 3 show up at most twice, and 5 show up at most once. The LCM is 2^1*3^2*5^1 = 2*9*5 = 18*5 = 90.

We'll use this LCM value to set up an example below.

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

Consider the tank to be 90 gallons. If we only use tap A, keep tap B closed, and don't open pipe C, then tap A fills the tank at a rate of 90/6 = 15 gallons per minute since it needs 6 minutes to completely fill the tank.

If we have tap B do all the work (keep tap A and pipe C closed), then the rate is 90/9 = 10 gallons per minute for this tap.

Keeping pipe C closed, the two taps A and B work together to have a combined rate of 15+10 = 25 gallons per minute.

Now we consider pipe C being opened. This drains the tank and can do so in 15 minutes (assume the taps A and B aren't open). If we're dealing with a full 90 gallon tank, then its rate is 90/15 = 6 gallons per minute.

The net rate is 25-6 = 19 gallons per minute. We can think of it as a tug of war where the taps A and B ultimately win out despite the fact that pipe C is draining the water. The two taps fill the tank faster than the pipe can drain the tank.

In other words, the tank ultimately gets filled up rather than drained out over the long run. That net speed is at 19 gallons per minute.

The amount of time needed is approximately 90/19 = 4.7368 minutes.

Side note: you can start with any size tank. It doesn't have to be 90 gallons. I picked on this value because it works cleanly with the original given numbers 6, 9 and 15.

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Answer:

No

Step-by-step explanation:

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Velocity: 300 mi/hr west, includes speed and direction

Acceleration: No, it does not say a starting speed or if it was a constant speed.

Hope this helps :)

7 0
3 years ago
Read 2 more answers
A restaurant manager has the option of a 30-year loan of $417,000 at an annual interest rate of 3.85% or the same interest rate
victus00 [196]

a) The monthly payment for each loan is as follows:

30-year $1,954.93

15-year $3,053.25

b) The savings in interest by using the 15-year loan is <u>$154,189,20</u> ($286,774.20 - $132,585).

c) No. the monthly payment for the 15-year loan is <u>not twice</u> that of the 30-year loan as the loan term.

d) The interest savings for the 15-year loan are <u>more</u> than one-half of the interest paid on the 30-year loan.

<h3>How are the calculations for periodic payments done?</h3>

The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:

<h3>30-year Loan:</h3>

N (# of periods) = 360 months (12 x 30 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

<u>Results</u>:

PMT = $1,954.93

Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)

Total Interest = $286,774.20 ($703,774.80 - $417,000)

<h3>15-year Loan:</h3>

N (# of periods) = 180 months (12 x 15 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

<u>Results</u>:

PMT = $3,053.25

Sum of all periodic payments = $549,585 ($3,053.25 x 180)

Total Interest = $132,585 ($549,585 - $417,000)

Learn more about periodic payments at brainly.com/question/13098072

#SPJ1

7 0
1 year ago
Find a polynomial equation that has double zeros at x = -3, and x = 4.
Digiron [165]

Answer:

Step-by-step explanation:

reqd polynomial=(x+3)²(x-4)^2

3 0
3 years ago
Calcular x en: los datos q faltan
Taya2010 [7]
Answer:

x = 13

Step-by-step explanation:

No se exactamente como decir esto porque yo ayudo la majoria de los usuario en ingles pero hay que usar un método para describir a x

Un método que se llama Pythagorean theorem

Pythagorean theorem: a^2 + b^2 = c^2 donde a^2 = 5 b^2 = 12 y c^2 = x

Entonces…

5^2 + 12^2 = c^2

Nota: podemos ver que esto esta bien porque el sum de los dos lados suma el mas largo.

Ahora

25 + 144 = c^2

c^2 = 169

Pero eso no puede ser la respuesta porque no tiene sentido a que x sea un lado que mide 169 entonces tenemos que usar sqrt rt

sqrt rt de 169 = 13

x = 13
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3 years ago
The average yearly precipitation for Gulfport,
ivanzaharov [21]
5.441 inches every month I’m pretty sure
8 0
3 years ago
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