Trees in alley

There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them?

Result

n =  27
x =  5 m

Solution:

35=57 15=35 95=519 GCD(35,15,95)=5  x=GCD(35,15,95)=5 m s=35+15+95=145 m  n0=s/x+1=145/5+1=30  n=n03=303=2735=5 \cdot 7 \ \\ 15=3 \cdot 5 \ \\ 95=5 \cdot 19 \ \\ \text{GCD}(35, 15, 95)=5 \ \\ \ \\ x=GCD(35,15,95)=5 \ \text{m} \ \\ s=35+15+95=145 \ \text{m} \ \\ \ \\ n_{0}=s/x+1=145/5+1=30 \ \\ \ \\ n=n_{0} - 3=30 - 3=27
x=5 mx=5 \ \text{m}



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