Quadratic Equations?

Question

a rectangular tank can be filled with water by 2 pipes in 11 and 1/9 mins. if the larger pipe alone takes 5 mins less to fill the tank than the smaller pipe, find the time each pipe takes to fill the tank.


can anyone help me on this?

Answer 1

20 and 25 minutes

Answer 2

Let x = time for the larger pipe, y = time for the smaller pipe, v = volume of the tank.

y - x = 5
(11 1/9)(v/x + v/y) = v

The first equation is obvious from the problem. The second may require explanation. v/x represents the rate at which water flows through the larger pipe since it can fill a container with volume v in x minutes. v/x + v/y represents the combined flow rate of the two pipes together. If we multiply the rate times the time it takes to fill the tank, we get the total amount of water (v) in the tank.

Reducing the second equation:
1/x + 1/y = 1/(11 1/9)
(x+y)/(xy) = 1/(11 1/9)

We know from the first equation that y = x + 5, so we plug that in to the above equation:

(x + x+5)/(x(x+5)) = 1/(11 1/9)
(2x+5)/(x^2 + 5x) = 1/(11 1/9)
Cross multiply:
(2x+5)(11 1/9) = x^2 + 5x
(200/9)x + 500/9 = x^2 + 5x
0 = x^2 -(155/9)x - 500/9

Solve this equation with the quadratic formula and you get: x=20 or x= -25/9. We want the positive one (x=20). Now that we have x, we plug it in to our first formula to get:

y - 20 = 5
y = 25

Our solutions are x=20, y=25. Lets check them by plugging them in to our two equations: y-x=5, and 1/x + 1/y = 1/(11 1/9).

25 - 20 = 5 (OK)

1/20 + 1/25 = 1/(100/9)
9/100 = 9/100 (OK)

We are done!

Answer 3

Larger pipe: 20 minutes
Smaller pipe: 25 minutes

First, call the time to fill for the larger pipe "x" and therefore for the smaller pipe "x + 5" and we're set. So, the pipes can, by themselves, do a portion of the job, 1/x and 1/(x+5), in one minute. Working together means we have to add those: 1/x + 1/(x+5) = (multiply by one in the forms of (x+5)/(x+5) and x/x) (2x + 5) / (x^2 + 5x). To find how many minutes they take together (which we know to be 11 1/9 (100/9)), divide 1 by the sum, or invert the fraction, to get: 100/9 = (x^2 + 5x) / (2x + 5). Multiply each side by 9 and (2x + 5) to get: 9x^2 + 45x = 200x + 500 and then rearrange terms so you have the standard quadratic equation form: 9x^2 -155x - 500 = 0. Plug in values (into the quadratic equation) and you get x = 20, -23/9. The negative answer doesn't apply here (!) so x, the time the larger pipe takes is 20 minutes and the smaller pipe takes 5 minutes more or 25 minutes.


Added:

raj has a mistep where he moved terms to the standard form. He was here:

adding -9x^2+45x
-9x^2+155x-500=0

But since he is adding +45x to the +200x it should have been 245x, not the 155x he shows and uses. With that in place, his path leads to x = 25 or 25 minutes for the smaller pipe and therefore 20 minutes for the larger one which would be right, of course. Just have to fix that one spot.

Answer 4

Let X an Y be the speed of each pipe, V the volume, s and t the time needed for each pipe. You have

(X+Y)x (100/9)=V. V/X =s = t-5 = V/Y -5 . Substituting you get 1+ (Y/X)=
1+(X/Y)- 9/20. If you let u= (X/Y) you obtain u^2 - 9/20 u -1 =0 so u =5/4. Therefore with the quicker one you need 9/5 of 11 , 1/9 that is 20 minutes and for the slower one you need 9/4 of 11, 1/9, that is 25 minutes, which is indeed how great! 20 +5

Answer 5

11 and 1/9 mins = 11*60+60/9 sec = 667 sec

x + y = 667
x + 5*60 = y

x + y = 667
x + 300 = y || y - 300 = x

y - 300 + y = 667
2*x-300 = 667
2*x = 967
x = 967/2

Answer 6

letthe time takenby the pipes be x min and x-5 min
the equation is
1/x+1/x-5=9/100
x-5+x=x(x-5)*9/100
multiplying by 100
100(2x-5)=9(x^2-5x)
200x-500=9x^2-45x
adding -9x^2+45x
-9x^2+245x-500=0
=>9x^2+245x+500=0
x=[245+/-rt(245^2-18000)]/18
=245+205/18
=450/18
the time taken bythe pies to fill the tank will be
25 minutes and 20 minutes

Answer 7

i forgot maths dear, especially quadratic eqn.
itz my fv8 subject n i forgot it, very bad na.

Answer 8

Why are you tring to get other people to do your work for you.

Answer 9

i could help if i were a stopwatch salesman

Answer 10

forget it