# Interesting Problem: Geometry

• Oct 28th 2010, 01:41 AM
rickrishav
Interesting Problem: Geometry
There is a cuboid room with dimensions 6m, 5m, 8m.
http://i876.photobucket.com/albums/ab324/rishavd/1.jpg
Find the shortest time taken by an ant inside the room, to go from A to B if the ant moves at a speed of 50cm/min
• Oct 28th 2010, 01:48 AM
Educated
Can the ant walk directly there? Or does it have to walk on the walls?

The shortest distance that it has to travel if it has to walk on the walls is diagonally from the 2 longest sides and directly from the shortest side.

So the distance that it has to walk is $\displaystyle \sqrt{6^2 + 8^2} + 5 = ...$
• Oct 28th 2010, 02:07 AM
brennan
Quote:

Originally Posted by rickrishav
There is a cuboid room with dimensions 6m, 5m, 8m.
http://i876.photobucket.com/albums/ab324/rishavd/1.jpg
Find the shortest time taken by an ant inside the room, to go from A to B if the ant moves at a speed of 50cm/min

If the back wall falls down that makes a length on the floor of (8+5) and 6 on a right angled triangle. The shortest distance must be the hypotenuse.

so $\displaystyle \sqrt{13^2 + 6^2}$

which is $\displaystyle \sqrt{205} = 14.3m$

So at 50cm/m this would take 26.6 minutes
• Oct 28th 2010, 04:40 AM
Soroban
Hello, rickrishav!

Quote:

There is a cuboid room with dimensions 6m, 5m, 8m.
Find the shortest time taken by an ant inside the room, to go from A to B
if the ant moves at a speed of 50 cm/min.

The ant will move right and upward on the front face,
then continue on the right face to $\displaystyle \,B.$

Code:

      * - - - - * - - - * B       |        |    *  |       |        | *    |       |        *|      | 8       |    *  |      |       |  *      |      |     A * - - - - * - - - *           6        5

The distance is: .$\displaystyle AB \:=\:\sqrt{11^2 + 8^2} \:=\:\sqrt{185} \:\approx\:13.6\text{ m}$

At 50 m/min, it will take 27.2 minutes.

• Oct 28th 2010, 05:16 AM
brennan
Quote:

Originally Posted by Soroban
Hello, rickrishav!

The ant will move right and upward on the front face,
then continue on the right face to $\displaystyle \,B.$

Code:

      * - - - - * - - - * B       |        |    *  |       |        | *    |       |        *|      | 8       |    *  |      |       |  *      |      |     A * - - - - * - - - *           6        5

The distance is: .$\displaystyle AB \:=\:\sqrt{11^2 + 8^2} \:=\:\sqrt{185} \:\approx\:13.6\text{ m}$

At 50 m/min, it will take 27.2 minutes.

      * - - - - * - - - * A       |        |    *  |       |        | *    |       |        *|      | 6       |    *  |      |       |  *      |      |   B * - - - - * - - - *           8        5