# Examples for 8th grade - page 103

- Overtaking

On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h.. - The farmer

The farmer had 140 sheep. For the next year, she decided to change the number of sheep in ratio 10: 7. How many sheep will he have then? - Find the 3

Find the distance and mid-point between A(1,2) and B(5,5). - Triplets

Three years ago, the triplets Pavel, Petr, and Luke and their five-year-old sister Jane had together 25 years. How old is Jane today? - Chocolate

I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate. - 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? - Two chords

There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure. - Cube

The sum of all cube edges is 30cm. Find the surface area of the cube. - Seawater

Seawater has a density of 1025 kg/m^{3}, ice 920 kg/m^{3}. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge. - Square

Square JKLM has sides of length 24 cm. Point S is the center of LM. Calculate the area of the quadrant JKSM in cm^{2}. - Height as diameter of base

The rotary cylinder has a height equal to the base diameter and the surface of 471 cm^{2}. Calculate the volume of a cylinder. - Highway tunnel

The highway tunnel was built from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" of the rasters. After 55 business days, both parties met. - Line segment

The 4 cm long line segment is enlarged in the ratio of 5/2. How many centimeters will measure the new line segment? - Irrigation sprinkler

The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can irrigate? - Circular arc

Calculate the length of the circular arc if the diameter d = 20cm and the angle alpha = 142 ° - Bricklayers

Seven bricklayers will build the house in 630 days. How many bricklayers do we need to take after 150 days to complete the building for (additional) 336 days? - Digit sum

How many are three-digit numbers that have a digit sum of 6? - Water reservoir

One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously? - Lunch

Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities? - The big clock

The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00.

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