A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Two pipe running together can fill a cistern in 3.5mins and one pipe takes 3 mins more than the other find the time in which each pipe would fill cistern
anonymous
 one year ago
Two pipe running together can fill a cistern in 3.5mins and one pipe takes 3 mins more than the other find the time in which each pipe would fill cistern

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino @pooja195 @perl

perl
 one year ago
Best ResponseYou've already chosen the best response.0Let x be the rate of the first pipe and y is the rate of the second pipe. And t be the time it takes for first pipe to fill cistern. Then we have the following equations, use d = r* t 1 cistern = (x+y) * 3.5 min 1 cistern = x * t 1 cistern = y * (t + 3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I can't understand the above.

perl
 one year ago
Best ResponseYou've already chosen the best response.0Have you used the formula distance = rate * time

perl
 one year ago
Best ResponseYou've already chosen the best response.0I am using a similar equation. 1 cistern = rate of pipe * time

perl
 one year ago
Best ResponseYou've already chosen the best response.0Let x be the rate of the first pipe and y is the rate of the second pipe. And t be the time it takes for first pipe to fill cistern. 1 cistern = (x+y) * 3.5 min 1 cistern = x * t 1 cistern = y * (t + 3)

perl
 one year ago
Best ResponseYou've already chosen the best response.0they are three different equations

perl
 one year ago
Best ResponseYou've already chosen the best response.0"Two pipe running together can fill a cistern in 3.5mins" That gives us 1 cistern = (x+y) * 3.5 min , where x and y are the rates of the pipes

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that @perl gave you the right explanation

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1nevertheless I can give you another way to solve your problem. The working rates of the two pipes are: \[\Large\frac{W}{x},\quad \frac{W}{{x + 3}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1where W is the work to be done

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, following the text of your problem, we can write: \[\Large \frac{W}{x} + \frac{W}{{x + 3}} = \frac{W}{{3.5}}\] and, simplifying that expression for W, we get: \[\Large \frac{1}{x} + \frac{1}{{x + 3}} = \frac{1}{{3.5}}\] Please solve that equation for x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x+3+x/x^2+3x = 1/3.5?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1first step: we have: \[\Large \frac{1}{x} + \frac{1}{{x + 3}} = \frac{2}{7}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! since 3.5= 7/2

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, the least common multiple, of x, x+3 and 7, is: x*(x+3)*7 am I right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1is that equation is equivalent to this one? \[\Large 1 \times 7 \times \left( {x + 3} \right) + 7x = 2x\left( {x + 3} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops..is that equation equivalent to this one?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1more steps: \[\Large \frac{{1 \times 7\left( {x + 3} \right)}}{{7x\left( {x + 3} \right)}} + \frac{{1 \times 7x}}{{7x\left( {x + 3} \right)}} = \frac{{2x\left( {x + 3} \right)}}{{7x\left( {x + 3} \right)}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1as denominator, of each fraction, we find the least common multiple

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, if we consider the first fraction, for example, we have: dw:1436624598950:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1similarly for the other 2 fractions

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1after that, we have to simplify the last equation, so we get: \[\Large 7x + 21 + 7x = 2{x^2} + 6x\] I have applied the distributive property of multiplication over addition Please rewrite that equation in this form: \[\Large bA{x^2} + Bx + C = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops.. in this form: \[\Large A{x^2} + Bx + C = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1what do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It should be 7x^2, right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: here are more steps: \[\Large \begin{gathered} 7x + 21 + 7x = 2{x^2} + 6x \hfill \\ 14x + 21 = 2{x^2} + 6x \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now I subtract 14 x from both sides so I can write: \[\Large 14x + 21  14x = 2{x^2} + 6x  14x\] please simplify

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: \[\Large \begin{gathered} 14x  14x = 0 \hfill \\ 6x  14x =  8x \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now you have to solve that equation, using the standard formula: \[\Large x = \frac{{  b \pm \sqrt {{b^2}  4 \times a \times c} }}{{2 \times a}}\] where \[\Large \begin{gathered} a = 2, \hfill \\ b =  8, \hfill \\ c =  21. \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Um? I can't use this formula as it's npt stated in the question *not

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1have you studied that formula in your course of mathematics?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep.. But my teacher would add "correct to 2 or 3 decimals" ONLY THEN can I use this formula.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then we can use that formula, here is the next step: \[\Large \begin{gathered} x = \frac{{8 \pm \sqrt {{{\left( {  8} \right)}^2}  4 \times 2 \times \left( {  21} \right)} }}{{2 \times 2}} = \hfill \\ \hfill \\ = \frac{{8 \pm \sqrt {64 + 168} }}{4} = ... \hfill \\ \end{gathered} \] please continue

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I would get this marked wrong if I use the formula... Please understand....

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1ok! I understand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I'll HAVE TO factor it out..

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1ok! I will write your next steps

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1If I divide both sides of your equation by 2, I get: \[\Large {x^2}  4x  \frac{{21}}{2} = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1Then I add and subtract 4 at left side, so I can write: \[\Large {x^2}  4x + 4  4  \frac{{21}}{2} = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1is it ok, for you?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now we note that: \[\Large {x^2}  4x + 4 = {\left( {x  2} \right)^2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we can rewrite my last expression as follows: \[\Large {\left( {x  2} \right)^2}  4  \frac{{21}}{2} = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1and, being: \[\Large  4  \frac{{21}}{2} = \frac{{  8  21}}{2} =  \frac{{29}}{2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have: \[\Large {\left( {x  2} \right)^2}  \frac{{29}}{2} = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now I add 29/2 to both sides of that equation, so I get: \[\Large \begin{gathered} {\left( {x  2} \right)^2}  \frac{{29}}{2} + \frac{{29}}{2} = 0 + \frac{{29}}{2} \hfill \\ \hfill \\ {\left( {x  2} \right)^2} = \frac{{29}}{2} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1ok! now I ask you, what is: \[\Large \sqrt {\frac{{29}}{2}} = ...?\] nearest to tenth?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow! @Michele_Laino perfect explanation :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1that's right! Now if I take the square rooth of both sides of my last equation, I get: \[\Large x  2 = \pm 3.8\] please remember we have 2 square roots

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1thanks!! @behappy

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we have 2 equations: \[\Large \begin{gathered} x  2 = 3.8 \hfill \\ \hfill \\ x  2 =  3.8 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! Nevertheless 1.8 can not be acceptable, since x represents a time. So only x=5.8 is the acceptable solution

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1finally the requested time are: \[\Large \begin{gathered} {t_1} = 5.8\min \hfill \\ {t_2} = 5.8 + 3 = ...\min \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0THANKS!!!!!! CAN YOU PLEASE HELP ME MORE?!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1thanks again for your appreciation to my work @behappy :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.