A frog (with webbed feet for sticking to a vertical surface) falls into a 6 ft deep hole with vertical sides. As the frog tries to escape, it is able to jump up 3 ft on a jump, but then slides back down 2 ft before it can jump again. If this continues, how many jumps will it take the frog to reach the top of the hole?

Question

Mathematics

Jovani Farmer

28 November, 15:24

A frog (with webbed feet for sticking to a vertical surface) falls into a 6 ft deep hole with vertical sides. As the frog tries to escape, it is able to jump up 3 ft on a jump, but then slides back down 2 ft before it can jump again. If this continues, how many jumps will it take the frog to reach the top of the hole?

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Answers (1)

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Allison · Answer 1

4

Step-by-step explanation:

Assuming that the frog is consistent with its performance, the correct answer can be calculated. It can be noticed that the ability to jump upwards is 3 feet and the sliding back down is 2 feet. This means that the gain is greater than the loss. The net gain is 1 foot for each jump. This will continue until the distance of 6 feet has been achieved. It will be: 3 ft - 2 ft = 1 ft (1 jump); 1 ft + 3 ft - 2 ft = 2 ft (2 jumps); 2 ft + 3 ft - 2 ft = 3 ft (3 jumps). At the end of the 3 jumps, the frog has already covered the distance of 3 feet. This means that when the frog jumps from this height, it will achieve the height of 6 feet, by which it will get out of the hole. This means that the frog requires 4 jumps to get out of the tunnel.