Trees in alley

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

Final Answer:

n =  26
x =  5 m

Step-by-step explanation:

$$\begin{gathered} a=35\text{m} \\ b=15\text{m} \\ c=95 \\ 35=5\cdot 7 \\ 15=3\cdot 5 \\ 95=5\cdot 19 \\ \text{GCD}(35,15,95)=5 \\ x=GCD(a,b,c)=GCD(35,15,95)=5\text{m} \\ s=a+b+c=35+15+95=145\text{m} \\ {n}_0=s/x+1=145/5+1=30 \\ n=n_0-4=30-4=26 \end{gathered}$$

$x=5=5\text{m}$

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