# Examples for 9th grade - page 49

- Two trains meet

From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B is 386 1/4 km. At what time and at what distance from B the two trains meet? - Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - Solution

What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture? - 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? - Power

Number ?. Find the value of x. - 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. - 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? - 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? - Dices throws

What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once - 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. - Unknown number

Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ

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