math challenge

Weeks of May 4 - 17, 1998

Xerxes on Xardu

On the planet Xardu, balls bounce in an unusual way.

Xerxes, a mischievous Xardutian, drops a ball from a window that is 40 meters off the ground. With the Nth bounce, it bounces up 1/N of the total distance.

The first bounce is (1/1)(40) = the entire 40 meters.
The second bounce is (1/2)(40) = 20 meters.
The third bounce is (1/3)(40) = 40/3 meters, etc.

How many meters will the ball have travelled (both up and down) after 10 bounces?

See the solutions