Question 983258
<font face="Times New Roman" size="+2">


Let *[tex \Large x] represent the number of minutes the small pipe takes to fill the tank.  Since we know this is 57 minutes longer than it takes the large pipe to fill the tank, the large pipe must take *[tex \Large x\ -\ 57] minutes.


So if it takes *[tex \Large x] minutes to fill the tank with the small pipe, then the small pipe can fill *[tex \Large \frac{1}{x}] of the tank in 1 minute.  Likewise, the large pipe would fill *[tex \Large \frac{1}{x\ -\ 57}] of the tank in 1 minute.  Since it takes 61 minutes working together, the two pipes working together can fill *[tex \Large \frac{1}{61}] of the tank in 1 minute.  Consequently:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{x\ -\ 57}\ =\ \frac{1}{61}]


I'll leave the algebra to you, but this simplifies to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 179x\ +\ 3477\ =\ 0]


Solve for the positive root.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \