Multiple choice general knowledge math & puzzles

A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder. How many rungs did the ladder have?

  1. 28

  2. 14

  3. 29

  4. 30
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Starting at the middle rung, the firefighter moves: +6 rungs up, -10 rungs down, then +18 rungs to reach the top. If the middle is rung m, then m + 6 - 10 + 18 = top rung. The middle of a 29-rung ladder is rung 14 (7 rungs below and 7 above). Starting from 14: 14 + 6 - 10 + 18 = 28, which is the top rung (rung 29). The ladder has 29 rungs total.

AI explanation

To solve this problem, let's break it down step by step.

Let's assume that the ladder has x rungs.

According to the given information, the firefighter stood on the middle rung of the ladder, which means that the middle rung is located at position (x + 1) / 2.

Next, the firefighter climbed up 6 rungs, so the new position of the firefighter is now at (x + 1) / 2 + 6.

After that, the firefighter came down 10 rungs, so the new position is (x + 1) / 2 + 6 - 10.

Finally, the firefighter climbed 18 rungs to reach the very top of the ladder, which means the new position is (x + 1) / 2 + 6 - 10 + 18.

According to the given information, the final position is equal to x, which means:

(x + 1) / 2 + 6 - 10 + 18 = x

Simplifying this equation, we get:

(x + 1) / 2 + 14 = x

Multiplying both sides of the equation by 2 to eliminate the fraction, we get:

x + 1 + 28 = 2x

Combining like terms, we get:

x + 29 = 2x

Subtracting x from both sides of the equation, we get:

29 = x

Therefore, the ladder has 29 rungs.

Hence, the correct answer is C) 29.

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