Destination 18323

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 Eva 50 cm. They went out on the same step. How many times did their steps retrace before reaching their destination?

Correct 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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