time and volumes help please!

Mar 2019
I have a question I am really stuck on; if anyone has any ideas?

A swimming pool can be filled by one hose in x days; or a different size hose in y days. It can be filled using both hoses together in m days.

Find a formula for m in terms of x &y, in its simplest form.

i have that that H1x = full pool. H2y = full pool; therefore h1x =h2y (both giving full pools).

for m - h1*m + h2*m = full pool.
so h1m+h2m = full pool

so h1m+h2m = h2y; and h1m+h2m=h1x

but i cant figure out where to go now - any ideas>
Dec 2014
[(hose 1 fill rate) + (hose 2 fill rate)] $\times$ (m days) = 1 pool filled

$\left( \dfrac{1 \text{ pool}}{x \text{ days}} + \dfrac{1 \text{ pool}}{y \text{ days}} \right) \cdot m \text{ days} = 1 \text{ pool filled}$

$\dfrac{m(x+y)}{xy}=1 \implies m = \dfrac{xy}{x+y}$