Solved Examples

Example 1: The Mine Shaft

Problem: A lift in a mine moves at a speed of 5 meters per minute. It starts from 10 meters above the ground.

1. Where will it be after 1 hour if it moves down?
2. How long will it take to reach -350 meters?

Solution

Part 1: Position after 1 hour

• Start Position: $+10$ m.
• Speed: $5$ m/min downwards ($-5$).
• Time: $1$ hour = $60$ minutes.
• Total Movement: $60 \times (-5) = -300$ m.
• Final Position: $\text{Start} + \text{Movement} = 10 + (-300) = -290$ m.
• Answer: 290 meters below ground.

Part 2: Time to reach -350m

• Target: $-350$.
• Start: $+10$.
• Distance to travel: $\text{Target} - \text{Start} = -350 - 10 = -360$ m.
• The lift must travel 360 meters down.
• Speed: 5m/min.
• Time: $360 \div 5 = 72$ minutes.
• Answer: 1 hour and 12 minutes.

Example 2: Magic Square

In a magic square, each row, column, and diagonal sums to the same number. Check if this is a magic square:

Check Rows:

1. $5 + (-1) + (-4) = 0$
2. $-5 + (-2) + 7 = 0$
3. $0 + 3 + (-3) = 0$

Check Columns:

1. $5 + (-5) + 0 = 0$
2. $-1 + (-2) + 3 = 0$
3. $-4 + 7 + (-3) = 0$

Check Diagonals:

1. $5 + (-2) + (-3) = 0$
2. $-4 + (-2) + 0 = -6$ (Wait! This is not 0).

Conclusion: Since one diagonal sums to -6, this is NOT a magic square.