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Chapter 1: Problem 62

India Jones is standing on a large rock in the middle of a square pool filled with hungry, man-eating piranhas. The edge of the pool is 20 feet away from the rock. India's mom wants to rescue her son, but she is standing on the edge of the pool with only two planks, each \(19 \frac{1}{2}\) feet long. How can India be rescued using the two planks?

Short Answer

Expert verified
India's mom can rescue him by assembling a bridge across the pool from one corner to the opposite corner using the two planks, then picking up India as she crosses the pool.

Step by step solution

01

Establish the situation

In the middle of a pool, there is a rock where India is standing. The edge of the pool is 20 feet away, and his mother has two planks, each measuring \(19 \frac{1}{2}\) feet.
02

Realize direct path is not possible

A direct path from the rock to the edge of the pool is not possible since it would require a distance larger than the planks' length.
03

Visualize the pool as a square with the rock at the center

This suggests that the rock is at the center of the square, and the edges of the square pool are the corners of the square.
04

Plan to reach a corner

Instead of going straight to the edge, India can target a corner of the pool. This would decrease the distance that they need to travel on the plank.
05

Calculate the corner to rock distance

Using the Pythagorean theorem, the distance from a corner to the center is \(\sqrt{20^2+20^2}\), which is approximately 28.3 feet. So, even reaching to a corner is not directly possible with the planks.
06

Make a bridge to a corner

The trick is to place the two planks end-to-end from one corner of the pool past the rock to the opposite corner. This way, the planks form a bridge of \(2\times19 \frac{1}{2} = 39\) feet, which is more than enough to cross the pool from one corner to another.
07

The rescue

Now, India's mom can walk to the middle of the plank bridge (to the rock), pick up India, then continue walking along the plank bridge to safety.

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