Family step retrace

The family went on a trip to a ruin 6 km away. The father had a step length of 0.75 m, the mother of 0.6 m, and little Eve 50 cm. They went out on the same step. How many times did their steps retrace before reaching their destination?

Final Answer:

n =  2000

Step-by-step explanation:

$$\begin{gathered} s=6\text{km}\to \text{m}=6\cdot 1000\text{m}=6000\text{m} \\ a=0.75\text{m}\to \text{cm}=0.75\cdot 100\text{cm}=75\text{cm} \\ b=0.6\text{m}\to \text{cm}=0.6\cdot 100\text{cm}=60\text{cm} \\ c=50\text{cm} \\ 75=3\cdot 5^2 \\ 60=2^2\cdot 3\cdot 5 \\ 50=2\cdot 5^2 \\ LCM(75,60,50)=2^2\cdot 3\cdot 5^2=300 \\ k=LCM(a,b,c)=LCM(75,60,50)=300\text{cm} \\ {k}_1=k\to \text{m}=k:100\text{m}=300:100\text{m}=3\text{m} \\ n=s/k_1=6000/3=2000 \end{gathered}$$

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