A tank of 425 litres capacity has been filled with water through two   pipes, the first pipe having been opened five hours longer than the   second. If the first pipe were open as long as the second, and the   second pipe was open as long as the first pipe was open, then the   first pipe would deliver half the amount of water delivered by the   second pipe; if the two pipes were open simultaneously, the tank would   be filled up in 17 hours. How long was the second pipe open?   I have solved this problem. But I need a shortcut method to solve this problem, the way which people would do in GMAT, CAT or other competitive exams where time is limited.  Attempt:  $$a(t+5)+bt=425 \tag 1$$  $$2at=b.(t+5) \tag 2$$  $$(a+b)*17=425$$  $$(a+b)=25 \tag 3$$  Solving these I got a quadratic equation:  $$15t^2-205t-300=0$$  $$t=15$$  Possible duplicate: How my question is different: I want a shortcut method to solve the problem. The answer to the previously asked question is not shortcut.
A tank of 425 liters capacity has been filled with water through two pipes, the first pipe having been opened 5 hours longer than the second. If the first pipe were open as long as the second pipe, the first pipe deliver half the amount of water delivered by second pipe; if the two pipes were open simultaneously, the tank would be filled up in 17 hours. How long was the second pipe open?    a. 10 b. 12 c. 15 d. 18
How to extend USB beyond the recommended maximum cable length of 5m? I'm planning to use USB port for an application(from a device to a PC) but the distance between the device and the PC will be around 15m. The recommended maximum USB cable length is 5m.  How can I buffer the data without loosing any information, safely? Would a USB hub work? What's the terminal command for finding out a process's id I want to exit a process using the command line, but I can't recall the command to look up the process's ID.  Does anyone know it? I always wondered on what algorihm the best league of mine is chosen.    I am in the 0.16% of this quarter. That is rank 171 this quarter. But I am also ranked 113th this month.  Why is the stat for the quarter displayed when I have a better ranking in the month? FileZilla: How to copy files from one directory to another on the same server? I want to copy files from one directory to another on the same server using FileZilla. Please guide me how can it be done? I am a mathematics student with a hobby interest in physics. This means that I've taken graduate courses in quantum dynamics and general relativity without the bulk of undergraduate physics courses and sheer volume of education into the physical tools and mindset that the other students who took the course had, like Noether's theorem, Lagrangian and Hamiltonian mechanics, statistical methods, and so on.  The courses themselves went well enough. My mathematical experience more or less made up for a lacking physical understanding. However, I still haven't found an elementary explanation of gauge invariance (if there is such a thing). I am aware of some examples, like how the magnetic potential is unique only up to a (time-)constant gradient. I also came across it in linearised general relativity, where there are several different perturbations to the spacetime metric that give the same observable dynamics.  However, to really understand what's going on, I like to have simpler examples. Unfortunately, I haven't been able to find any. I guess, since "gauge invariance" is such a frightening phrase, no one use that word when writing to a high school student.  So, my (very simple) question is: In many high school physics calculations, you measure or calculate time, distance, potential energy, temperature, and other quantities. These calculations very often depend only on the difference between two values, not the concrete values themselves. You are therefore free to choose a zero to your liking. Is this an example of gauge invariance in the same sense as the graduate examples above? Or are these two different concepts? Advanced search criteria for bounty questions? All active questions with awarded bounty can be seen in the Featured tab. However, there seems to be way to make searches to the contents of any particular question tab.  I realize that this is pretty much a duplicate of  but it has no clear answer whether there are any plans of supporting bounty searching or not.  So, could there possibly be a hasbounty:1 advanced search criteria? What does it mean to "program to an interface"? How do I bridge network interfaces? I have a laptop running 11.10 with 2 network interfaces, wired and wireless.  Wireless interface connects to the router with DHCP and connects to the internet. Wired interface is connected to a switch. I want the computers on the switch to get their IP addresses from the router not my laptop.     How would I go about setting this up? Bridging the interfaces? The only 1-manifolds are $\mathbb R$ and $S^1$ I recall having heard somewhere that the only 1-manifolds (second countable, Hausdorff, connected spaces locally homeomorphic to $\mathbb R$) are $\mathbb R$ and $S^1$. Is this true? If so, is there a reasonably elementary proof? What should I do if I want to be able to run a given program regardless of my current directory? Should I create a symbolic link to the program in the /bin folder? I'm trying to load a field value (machine name: field_theme_image) from a content of node value 3, in "page--front.tpl.php".  &lt;?php   $node=node_load(3);   print $node-&gt;field_theme_image[$node-&gt;language][0]['uri']; ?&gt;   Using the above code I'm not getting full URL value. Please see the image below. I can see the path value in Devel themer. Modular Arithmetic - Find the Square Root Make Javascript do List Comprehension Are any of the USB ports on a Macbook Pro "always on" Always on USB ports will provide power to a device even when the laptop is shut down. Obviously this can be problematic for battery issues, but sometimes a user wants this capability all things considered.  Do the Macbook Pro offer this on any of the USB ports and if not is there any chance its wired and just has to be enabled? Redirect the output using `sudo` I have a small question regarding using sudo with output redirect &gt;. To enable IP forwrding, someone can use the command:  echo 1 &gt; /proc/sys/net/ipv4/ip_forward   Executing this command will give permission denied as it requires root privileges. However, executing the same command with sudo gives also permission denied error! It seems that output redirect &gt; does not inherit the permissions of the preceding command echo. Is this right?  As a workaround I do:  echo 1 | sudo tee /proc/sys/net/ipv4/ip_forward   Is this the best way to do it? Am I missing something?  Please, note that this is an example and it applies to all commands that use output redirect. django manytomanyfield .add() method In the sentence: "Drinking and driving IS dangerous", why does the verb "to be" need to be singular? In the sentence: "Drinking and driving is dangerous". Drinking and driving are both subjects and the word dangerous is the object (I think) but why do I have to use the verb to be in singular? I know how to use the subfig package to fit many subfigures (each with its own caption) into a larger figure (with a general caption).  I know how to use the sidecap package, the put a figure's caption on the side of the figure.  What I do not know is how to display a caption inside the figure, as if it were a subfigure.  More precisely, I have three subfigures that I would like to fit on a 2x2 layout, with the remaining quadrant used for the caption.    Is that easy to achieve? titlesec: loss of section numbering with the new update (2016/03/15) After reinstalling TeXLive distribution (install-tl-20160318, Ubuntu 14.04), a issue occurs with the updated version of the titlesec package: the section numbering is lost.  What could it be missing? Is there a modification I have not seen?  Below is a MWE comparison of the two versions. The prevtitlesec package is a reinstall of the previous version (2011/12/15).  \documentclass{book} \usepackage[margin=2cm,a4paper]{geometry} %\usepackage{prevtitlesec}% 2011/12/15 version \usepackage{titlesec}% 2016/03/15 version \usepackage{lipsum}  \begin{document}  \chapter{Title of the first chapter} \lipsum[1] \section{A test section} \lipsum[4] \subsection{A test subsection} \lipsum[4] \subsection{A test subsection} \lipsum[4]  \end{document}   titlesec package 2011/12/15:    titlesec package 2016/03/15: BibTeX bibliography not printing I was unable to find a previous post about this - perhaps too simple? I just came across the BibTeX and am trying to use it with an EndNote library. I have exported to the .bib file (which looks good as far as I can tell), but no bibliography is printed and the references aren't being cited. Obviously there is something major missing.  My document looks as follows.  \documentclass[11pt, fceqn]{article} \usepackage{epsfig} \usepackage{setspace, titlesec, caption, floatrow}    \usepackage{amsmath, amssymb, amsfonts, amsthm, cite, mathtools, lineno, subfig, natbib}  \begin{document}   Some text \cite{Alo_1}.  \bibliography{bib} \bibliographystyle{plain}  \end{document}   Any thoughts would be greatly appreciated.