Question 935746
THE ANSWER IS "YES" YOU HAVE ARRIVED AT THE CORRECT EQUATION TO SOLVE BUT I'M NOT SURE WHAT YOU RATIONALE WAS. :) 

Let t=amount of time it takes both pipes to finish filling the pond
First pipe fills at the rate of 1/10 of the pond per hour
Second pipe fills at the rate of 1/12 of the pond per hour
After 5 hours, first pipe fills (1/10)*5=5/10 = 1/2 of the pond leaving 1/2 of the pond yet to be filled.

So both pipes working together fills at the rate of 1/10 + 1/12=6/60+5/60=11/60 of the pond per hour.

Our equation to solve then is:
(11/60)*t=1/2
Or we can write the equation this way:
t/10 + t/12 = 1/2 which is exactly what you have.


Hope this helps----ptaylor