Walk for exercise

Anya, Jose, Cali, and Stephan walk for exercise. Anya's route is 2 1/4 kilometers long. Jose's route is 1 1/2 fewer km. Cali's route is 1 1/2 times as long as Jose's route and two fewer km than Stephan's route.

What distance (S) is Stephan's route?

Final Answer:

S =  3 ¹⁄₈ = 25/8 km

Step-by-step explanation:

$$\begin{gathered} A=2\frac{1}{4}=2+\frac{1}{4}=\frac{2\cdot 4+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2.25\text{km} \\ J=A-1\frac{1}{2}=\frac{9}{4}-1\frac{1}{2}=\frac{9}{4}-\frac{3}{2}=\frac{9}{4}-\frac{6}{4}=\frac{9-6}{4}=\frac{3}{4}=0.75\text{km} \\ C=1\frac{1}{2}\cdot J=1\frac{1}{2}\cdot \frac{3}{4}=\frac{3}{2}\cdot \frac{3}{4}=\frac{3\cdot 3}{2\cdot 4}=\frac{9}{8}=1.125\text{km} \\ C=S-2km \\ S=C+2=\frac{9}{8}+2=\frac{9}{8}+\frac{2\cdot 8}{8}=\frac{9}{8}+\frac{16}{8}=\frac{9+16}{8}=\frac{25}{8}=\frac{25}{8}\text{km}=3\frac{1}{8}\text{km}=3.125\text{km} \end{gathered}$$

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