To a bath there are two taps:
one - fill the bath half an hour.
the second - fill the bath third of the hour.
The taps open together.
What the time the bath will be filled about?
x = time in hours both taps work together
rate 1 = how many baths tap 1 fills in one hour
rate 2 = how many baths tap 2 fills in one hour
1 = the whole job
x(rate 1 + rate 2) = 1
x(2 + 3) = 1
5x = 1
x = 1/5
1/5 hour
or
12 minutes
Or: "one - fill the bath half an hour" fills the bath at the rate of 2 baths per hour.
"the second - fill the bath third of the hour" fills the bath at the rate of 3 baths per hour.
Together, they fill the bath at the rate of 2+ 3= 5 baths per hour.
That is a rate of 1/5 hour per bath or 60/5= 12 minutes to fill one bath.
What do you get if you add those? 1/2 hour to fill the bath+ 1/3 hour to fill the bath= 3/6+ 2/6= 5/6 hour per bath, almost an hour. Does it make sense that using both taps it would take longer to fill the bath than only one?
A rate is 'progress (distance, filling a bath, doing a job, whatever) per hour'. You need to invert to get 2 and 3 baths per hour.