If it rains harder, does it mean the rain's duration will be shorter?
The intensity of a rainstorm does not actually cause the duration of the precipitation to be shorter. There is a strong correlation, but not in the sense you may be implying here (let me get back to that in moment).
First you have to dispel the model that a cloud is a big container of water, and if it &quot;rains harder&quot;, the cloud will run out of water quicker and the rain event will be shorter in duration. Rain doesn't really work like that.
The atmosphere everywhere (even outside the cloud) contains lots and lots and lots of water. And under a stable combination of temperature, pressure, and humidity, all that moisture is perfectly happy to exist in a completely gaseous state. But as differing air masses (different temperatures, pressure, and humidity) start to collide, the local atmospheric conditions can fall outside the range where water can exist in a completely gaseous state. That is known as the dew point.
A cloud is where two differing atmospheric conditions have met, and the resulting condensed water droplets simply do not have sufficient weight to overcome the updraft speed of the air around it. If the air masses mix slowly, the rate of condensation will occur slowly and over a longer period of time. The resulting clouds may simply &quot;evaporate&quot; as the local conditions stabilize, or the condensing water may slowly precipitate over the ground (gentle rain), or the precipitation may never reach the ground at all (virga). These gentler atmospheric changes tend to play out over longer periods of time because the air masses are moving more slowly so it takes longer for the differences to mix and settle down into a new steady state.
Here's the part where I talk about intensity
If two air masses have widely varying conditions (think warm moist air over the ocean meeting dryer hotter conditions over the land) and they meet more abruptly (higher wind speeds), this causes a more-violent disturbance; the moisture from the air will condense more quickly, the rain falls faster and harder, and the whole thing ends (relatively speaking) more quickly.
But the duration tends to be shorter because the reaction between the differing masses is occurring at a faster rate — so the whole event will generally play out more quickly. But it is perfectly conceivable that &quot;harder rain&quot; can last much longer if the storm system continues to pull in more of the moist atmosphere around it. In extreme circumstances, that's pretty much what a hurricane is; the storm itself gets so big that it starts to create it's own system that pulls in more and more atmosphere around it. The rain doesn't simply stop when all the rain has fallen out of the original clouds. It actually (continually) makes new clouds/precipitation as it continues to draw in the atmosphere surrounding it.
But speaking in broad generalities, the faster the disturbance occurs, the faster the moisture will condense, the harder the precipitation will fall, the more quickly the conditions will stabilize, and the duration of the rain will be less.