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How long will it take?


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There is a pool of water that, when in full sunlight, increases in temperature by one degree Celsius in ten minutes.

At 12:00pm the pool is half covered by the shade of a tree. And by 13:00pm the pool is in full sun. (So that between 12 and 1 pm the pool is partially cover by some shade.) It can be assumed that the shade covers half the pool at 12:30 and so on.

If the pool of water is 28 degree Celsius at 11:50am, how long will it take to increase it 32 degrees Celsius?

If half the pool is covered by shape it will take twice as long to incease by one degree.

Between 11:50am and 12:00pm by pool will be cover by some shade.

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The problem states that "At 12:00pm the pool is half covered by the shade of a tree" and again later states that "It can be assumed that the shade covers half the pool at 12:30". Is the pool HALF covered by the shade at 12:00 or 12:30? Please clarify.

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It would also be nice to give us the shape of the pool since even a simple circular pool would not have a linear decrease in proportional shade coverage over time whereas a rectangular pool aligned with the sun and the tree (all factors must be exact) would result in a linear change in shade coverage. Depths would also need to be constant (and shallow) for the temperature change to be the same across the entire pool. Are we also to assume there isn't evaporation?

Edited by Egghead
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There is a pool of water that, when in full sunlight, increases in temperature by one degree Celsius in ten minutes.

At 12:00pm the pool is half covered by the shade of a tree. And by 13:00pm the pool is in full sun. (So that between 12 and 1 pm the pool is partially cover by some shade.) It can be assumed that the shade covers half the pool at 12:30 and so on.

Should this be "fully covered" instead of "half covered"?

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Sorry. I was very tired when I wrote the question.

It should have been that at 12:30 the shade covers half the area that the shade covers at 12:00, i.e. a 1/4 of the whole pool. The pool also has the same depth throughout.

And there is no evaporation.

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The question did ask how long will it take.

It will take 59 min and 5 sec. (or at the time of 12:49:05)

But since the question did not say anything about seconds, I will accept Peekay answer as correct. Well done.

This was my first question I posted, hope it was okay.

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