Step-by-step 8273

On a map with a scale of 1:500,000, the aerial distance is equal to 12 cm. The distance by rail is equal to 100 km. The road distance is 92 km. Express the air, rail, and road distance in a step-by-step ratio.

Correct answer:

p = 15:25:23

Step-by-step explanation:

$$\begin{gathered} v_1=12\text{cm}\to \text{km}=12:100000\text{km}=0.00012\text{km} \\ {s}_1=v_1\cdot 500000=0.0001\cdot 500000=60\text{km} \\ {s}_2=100\text{km} \\ {s}_3=92\text{km} \\ p=s_1:s_2:s_3 \\ p=60:100:92 \\ 60=2^2\cdot 3\cdot 5 \\ 100=2^2\cdot 5^2 \\ 92=2^2\cdot 23 \\ \text{GCD}(60,100,92)=2^2=4 \\ k=GCD(60,100,92)=4 \\ p=15:25:23 \end{gathered}$$

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