Why does water takes longer to cool than it takes to boil

It's about the temperature change desired, and the temperature difference between the hot/cold object and the source of cooling/heating.

Suppose in heating, we boil 20 C water over a 1000 C flame until it reaches 100 C, and in cooling we cool 100 C water on a 0 C cold plate until it reaches 20 C.

So in heating we have a 980 C temp diff to drive an 80 C temp change, while in cooling we have a 100 C temp diff to drive an 80 C temp change. Big difference!

I would think it does not.

If you heat the water slowly, it can take a long time to boil. If you put it outside at 40 below zero, it cools fast.

When you boil water, the time is proportional to the amount of heat used. If you are cooling it, the time depends on how cold the chamber is that you cool it in.

When you boil the water, the water is under the flame, so it is boiling faster. When you want the water to cool down faster, it is hard. The water needs to cool down by puting some ice, putting in cool environment and so on, if not, it will cool down slowly.

It probably has something to do with the conductive properties of the medium through which the heat is transferred. When we heat water it, or its container, is usually in direct contact with an element or hotplate. Both of these things conduct heat to the water quite efficiently. When we place water into a cooler area such as a refrigerator we are relying on conduction through the air, which is much less efficient and the heat transfer is slower.

this sounds like a trick question. putting heat into something will take just as long as taking it out of something (unless you change the characteristics of the container it is in: e.g. passing it through a radiator). this is most likely a myth that you are asking about. but, remember pure water freezers at about 32F at sea level but thaws at about 36F. it is weird stuff. no one, no one, really understands why it works the way it does.