How Far Did I Run?

I leave my front door, run on a level road for some distance, then run to the top of a hill and return home by the same route. I run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. 

If my total trip took 2 hours, how far did I run?

I ran the distance.....Click here for more!

Calculation of Avarage Speed is Tricky!

First read what was the question!

Let's first find my average speed when I was running uphill & downhill.

Assume 'x' be the distance that I have to run to reach at the top of the hill in time 'y'.

So x/y = 6 mph.

While running downhill, I cover same distance 'x' in time 'y/2' as I ran at double speed of 12 mph.

Average speed = Total Distance / Total Time

Average speed = (x + x) / (y + y/2)

Average speed = (4/3)(x/y)

Average speed = (4/3) x 6

Average speed = 8 mph.

That means my average speed on hill is equal to the my speed on level ground and that is 8 mph.

Since I ran for 2 hours in my trip the distance I ran is 8 x 2 = 16 miles.

How it Will Affect the Water Level?

A man stuck in a small sailboat on a perfectly calm lake throws a stone overboard. It sinks to the bottom of the lake.

When the water again settles to a perfect calm, is the water level in the lake higher, lower, or in the same place compared to where it was before the stone was cast in?

Did you think it will rise? 

Physics : Finding the Effect on the Water Level

But why water level was affected?

Do you recall what does Archimedes Principle state? For an object to float on water, it has to displace that much volume of water whose weight is equal to weight of the object itself. Now if object has less density than water then obviously it has to displace lesser amount of volume of water to float on it. That means it has to sink less in water.

For a moment, let's assume the stone has very high density & hence having weight equal to hundreds of kilograms despite of having small volume.

Here, stone sinks to the bottom of the lake suggests that it is has more density than water. It can't displace the water whose weight is equal to it's weight.But when it was on sailboat it could push the sailboat down so that more water is displaced weighing equal to it's weight. Result of this, the sailboat sinks little 'deeper' compared to when stone wasn't there.

Obviously, the volume of displaced water when stone was in sailboat (due to stone only) must be greater that the volume of displaced water when stone sinks to the bottom of the lake. That's why both sailboat and stone together could float on the water. In short, sailboat helped stone to displace amount of water needed to float which results in rise in shoreline.

And when stone is thrown out of the sailboat, then ideally it can't displace more water than when it was on sailboat. Now, sailboat sinks less 'deeper' in water displacing only water need to float itself. 

That's why the water level must be dropped compared to earlier. The little rise due to water displaced by stone can't exceed the earlier water level for the reason explained above.