Discussion
A frog tries to come out of a 30 m deep dried well with slippery walls. In every jump the frog jumps up by 70 cm, but slides down 30 cm. What is the minimum number of jumps required for the frog to come out of the well?
Answer: C
The frog needs 75 jumps.
Each full jump-and-slide gains \(70 - 30 = 40\) cm. But on the final jump the frog leaves the well and does not slide back, so stop counting slides before the last jump.
\[ \begin{aligned} 40(k - 1) + 70 &\ge 3000 \\ k - 1 &\ge 73.25 \Rightarrow k = 75 \end{aligned} \]
After 74 jumps (and slides) the frog is at \(74 \times 40 = 2960\) cm, and the 75th jump of 70 cm takes it to 3030 cm, out of the well. Dividing 3000 by 40 gives exactly 75 here, but only by coincidence; 76 and 78 come from ignoring the last-jump rule in other ways, and 73 stops short.
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