# Draw a Diagram and Solve a Simpler Problem

## Lesson Preview

### What You'll Learn

1. To solve a problem using two different methods

### … And Why

To compare strategies in problem solving, as in Example 1

## Solving a Problem Using Two Different Methods

When to Use These StrategiesYou can draw a diagram to show a problem visually. For problems that seem to have an overwhelming number of steps, you can solve a simpler problem that is similar. These strategies are used as alternative methods in Example 1.

#### Using Strategies

A worm is trying to escape from a well 10 ft deep. The worm climbs 2 ft per day, but each night it slides back 1 ft. How many days will the worm take to climb out of the well?

The total distance to travel is 10 ft. The worm gains 2 ft during the day, but loses 1 ft each night. The goal is to find out how many days the worm will take to get out of the well.

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Method 1 Draw a Diagram

Draw a diagram, such as the one at the right, that allows you to track the worm's position from day to day.

The worm reaches 10 ft and climbs out of the well at the end of the ninth day.

Method 2 Solve a Simpler Problem

Instead of solving the problem for a 10-ft well, change the problem to a simpler one based on a 3-ft well, and then on a 4-ft well.

The worm will take 2 days to climb out of a 3-ft well and 3 days to climb out of a 4-ft well. So it would take 9 days to climb out of a 10-ft well.

Your first thought might have been that the worm progresses 1 ft each day and therefore needs 10 days to escape. The worm does move a total of 1 ft each day, except on the ninth day. On the ninth day it climbs 2 ft and reaches the edge of the well.