Melody

"any one mathematical operator"     -      any one means ONLY one 

That is a quote from the question.  

It doesn't matter though - I liked your answer  :)

I like you second answer too.

I would like to see anon do it with ony one operator as well    LOL

@@ End of Day Wrap   Wed 20/5/15   Sydney, Australia Time   12:30am  (Thurs really) ♪ ♫

Hi all, 

Great answers today from:  Alan, CPhill, Andrew1714, TheJamesMachine, Dbg4thebest, MathsGod1, DarkBlaze347, ShadowBolt04, Zacismyname, Heureka, GoldenLeaf, MathWitch and Badinage.  Thank you. 

Thurs 21/5/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

Interest Posts:

FTJ means 'For the juniors' 

Hi Nauseated,

Zac's hemisphere and my hemisphere had a bottom on it.

A hemisphere is a half of a sphere - if the sphere is solid then the hemisphere definitely has a base.

Our brains have ceribral hemispheres.  

Mine is full of grey matter.   Does yours is contains nothing?

Did you struggle with that one for as long as I did Chris?

I have done heaps of these but they turn into a saga EVERY time.    LOL

Oh well I got there in the end, CPhill and I did it a bit differently but we both got the same answer.

That is always a good sign   

2 taps A and B can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 5 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool?

A is the fast one:   let tap A take X hours to fill the pool

A fills 1 pool in X hours

that is 3 pools in 3X hours   OR      3/X pools in 3 hours

B fills 1 pool in X+5 hours

that is 3 pools in 3(X+5) hours    OR        3/(X+5) pools in 3 hours

So together in 3 hours they will fill

$$\frac{3}{X}+\frac{3}{X+5} \;\;pools\\\\
=\frac{3(X+5)+3X}{X(X+5)}\;\;pools\; in\; 3 \;hours\\\\
$But in 3 hours they fill 1 pool so $\\\\
\frac{3(X+5)+3X}{X(X+5)}=1\\\\
3(X+5)+3X=X(X+5)\\\\
3X+15+3X=X^2+5X\\\\
6X+15=X^2+5X\\\\
X^2+5X-6X-15=0\\\\
X^2-X-15=0\\\$$

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{15}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{61}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.405\: \!124\: \!837\: \!953\: \!327\: \!2}}\\
{\mathtt{x}} = {\mathtt{4.405\: \!124\: \!837\: \!953\: \!327\: \!2}}\\
\end{array} \right\}$$

Obviously the negative answer is invalid  so X = 4.4051 hours to fill the pool

$${\mathtt{60}}{\mathtt{\,\times\,}}{\mathtt{0.405\: \!1}} = {\mathtt{24.306}}$$

So that is near enough to 4 hours and 24 minutes

A will take 4 hours and 24 minutes to fill the pool

and

B will take 9 hours and 24 minutes to fill the pool.

little triangles can mean a small change in something  

Or a little triangle is used for the discriminant in the quadratic formula

Or it may actually mean triangle   lol

WHAT IS A TARDIS YOU ASK !

The median is the middle number so ...

Let the numbers be A, 7, B

(A+B+7)/3 = 5

A+B+7=15

A+B=8

now remember that A and B are whole positive numbers and    $$A\le7\le B$$

So the only possible numbers are    1,7,7

The range is 7-1=6

There is no biggest number