To solve this problem, we must determine how many jumps the frog needs to make to get out of the 30-meter deep well.
- The frog jumps up \(70 \text{ cm}\) on each jump and then slides back down \(30 \text{ cm}\).
- The effective height gained after each jump is: \(70 \text{ cm} - 30 \text{ cm} = 40 \text{ cm}\)
- First, convert the depth of the well to centimeters: \(30 \text{ m} = 3000 \text{ cm}\)
- Determine how many effective jumps of \(40 \text{ cm}\) each are needed to reach just below the rim of the well: \(\frac{3000 \text{ cm}}{40 \text{ cm per jump}} = 75 \text{ jumps}\)However, with 75 full jumps, let's consider the scenario:
- After 74 jumps, the frog would have climbed: \(74 \times 40 \text{ cm} = 2960 \text{ cm}\)
- This means at the start of the 75th jump, the frog is 2960 cm up, requiring one more \(70 \text{ cm}\) jump to finish the climb without slipping back again.
Therefore, the minimum number of jumps required for the frog to completely get out of the well is 75.
Summary: The frog effectively gains \(40 \text{ cm}\) per jump, and after 74 jumps, it is at 2960 cm. The 75th jump allows it to reach the top.
Important Questions from Quick Math
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