Question

In a well, there are two lizards, Red and Green. Both start climbing a slimy wall at the same time. In each attempt, Green climbs three feet up and slides one foot down, whereas Red climbs four feet up and slides two feet down. If the height of the wall is 10 feet, who will reach the top of the wall in fewer attempts?

• A. None will reach the edge
• B. Green lizard
• C. Red lizard
• D. Red and Green lizards will take the same number of attempts

Hint:

To solve such problems, calculate the net progress of each lizard and determine how many attempts it will take to reach the top.

Answer 1

The Correct Option is C

Step 1: Analyzing the Green lizard's progress.
In each attempt, the Green lizard climbs 3 feet and slides 1 foot back. Thus, in each attempt, the net progress is 2 feet (3 feet up - 1 foot down). After 4 attempts, the Green lizard will have climbed: \[ 4 \times 2 = 8 \, \text{feet} \] In the 5th attempt, it climbs 3 feet and reaches the top, for a total of 10 feet.
Step 2: Analyzing the Red lizard's progress.
In each attempt, the Red lizard climbs 4 feet and slides 2 feet back. Thus, in each attempt, the net progress is 2 feet (4 feet up - 2 feet down). After 3 attempts, the Red lizard will have climbed: \[ 3 \times 2 = 6 \, \text{feet} \] In the 4th attempt, the Red lizard climbs 4 feet and reaches the top, for a total of 10 feet.
Step 3: Conclusion.
The Red lizard reaches the top in fewer attempts (4 attempts) compared to the Green lizard (5 attempts).
\[ \boxed{(C) \, \text{Red lizard}} \]