# Examples for 8th grade - page 53

- Two months

Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies? - Rectangular field

One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m^{2}. Determine dimencions of the field. - Interest p.a.

Calculate the value of interest in period of 1 year from the deposit 62000 CZK at 8 percent interest rate, after deducting 15 percent tax. - Cars speeds

Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes? - Alfa, beta, gama

In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC. - Square vs rectangle

Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square. - Extreme temperatures

USA hit extreme heat wave. Calculate percentage of the air temperature change from normal summer temperature 23 °C to 40 °C. - Three men

Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old? - Obtuse angle

The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Ratio of two unknown numbers

Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given? - Travel by bus

Five girls traveling by bus. Each holds in each hand two baskets. Each basket contains 5 cats. Each cat has 5 kittens. 3 girls getting off the bus and another girl without baskets go on board. The bus control driver. How many legs are in the bus? - Fifth of the number

The fifth of the number is by 24 less than that number. What is the number? - Arc-sector

arc length = 17 cm area of sector = 55 cm^{2}arc angle = ? the radius of the sector = ? - Cargo

Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load? - Crown coins

Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns? - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Tray

Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm. - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Saw

Blade circular saw with a diameter 42 cm turns 825 times per minute. Expresses his cutting speed in meters per minute. - Sputnik

The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round?

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