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?

Correct result:

n =  27
x =  5 m

Solution:

$$\begin{gathered} 35=5\cdot 7 \\ 15=3\cdot 5 \\ 95=5\cdot 19 \\ \text{GCD}(35,15,95)=5 \\ x=GCD(35,15,95)=5\text{ m } \\ s=35+15+95=145\text{ m } \\ {n}_0=s\mathrm{/}x+1=145\mathrm{/}5+1=30 \\ n=n_0-3=30-3=27 \end{gathered}$$

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

Try another example

Showing 0 comments:

Next similar math problems:

• Four poplars
  Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
• Garden
  The garden has the shape of a rectangle measuring 19m20cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent p
• Paving - joints
  We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and in the second row in width etc. How many times will the joints meet at a distance 10 m?
• Florist
  Florist has 84 red and 48 white roses. How many same bouquets can he make from them if he must use all roses?
• Apples and pears
  Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child?
• Glass panel
  A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
• Groups
  In the 6th class there are 60 girls and 72 boys. We want to divide them into groups so that the number of girls and boys is the same. How many groups can you create? How many girls will be in the group?
• Birthdate
  Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?
• Plumber
  Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
• School year
  At the beginning of the school year, 396 notebooks and 252 textbooks are ready to be distributed in the classroom. All pupils receive the same number of notebooks and the same amount of textbooks. How many pupils are there in the class if you know that th
• Pegs
  From two sticks 240 cm and 210 cm long, it is necessary to cut the longest possible pegs for flowers so that no residues remain. How many pegs will it be?
• 9.A
  9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
• Three friends
  Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
• Around the flowerbed
  Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros
• Fewer than 500 sheep,
  There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
• Meadow
  On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together?