Hare 2024m

A hare participated in a race 2024 metres long. From the starting line he pushed off with his left foot and throughout the race he regularly alternated left, right, and both feet. When the hare pushed off with his left foot, he jumped 35 dm, when he pushed off with his right foot, he jumped 15 dm, and when he pushed off with both feet, he jumped 61 dm. How many jumps did the hare make before reaching the finish line? With which foot did he push off at the finishing jump?

Final Answer:

n =  548
w = P

Step-by-step explanation:

$$\begin{gathered} a=2024\text{m}\to \text{dm}=2024\cdot 10\text{dm}=20240\text{dm} \\ l=35\text{dm} \\ p=15\text{dm} \\ s=61\text{dm} \\ k=l+p+s=35+15+61=111 \\ {n}_1=a/k=20240/111\doteq 182.3423 \\ {n}_2=\lfloor n_1\rfloor =\lfloor 182.3423\rfloor =182 \\ {a}_1=n_2\cdot k=182\cdot 111=20202\text{dm} \\ {b}_1=a-a_1=20240-20202=38\text{dm} \\ l \\ {b}_2=b_1-l=38-35=3\text{dm} \\ p \\ {b}_3=b_2-p=3-15=-12\text{dm} \\ n=n_2\cdot 3+2=182\cdot 3+2=548 \end{gathered}$$

$$\begin{gathered} b_3<0 \\ w=P \end{gathered}$$

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