# Examples for 9th grade - page 45

- Harvesters

The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first? - Coins

On coins found was stated that from the year 87 BC. It is right? - Two pumps

The first pump fills the tank in 24 hours second pump in another 40 hours. For how long will take fill the tank if operate both pumps at the same time? - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ? - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Angles

The outer angle of the triangle ABC at the vertex A is 114°12'. The outer angle at the vertex B is 139°18'. What size is the internal angle at the vertex C? - Medians in triangle

Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm. - Antennas

If you give me two antennas will be same. If you give me again your two antenna I have a 5× so many than you. How many antennas have both mans? - Coffee

Coffee merchant has coffee robusta and arabica species. 1 kg Robusta worth 450 CZK, Arabica 1 kg is 300 CZK more expensive. Calculate how many kilograms of Robusta and Arabica will need to produce 30 kg of the mixture so that the mixture cost is 490 CZK p - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Otto and Joachim

Otto and Joachim go through the woods. After some time Otto tire and make 15 minutes stop. Joachim meanwhile continues at 5 km/h. Otto when he set off again, first running speed of 7 km/h, but it keep only 30 sec and 1 minute must continue at 3 km/h. This. - Painters

One painter could paint a school for 7 days. The second one for 6 days. It was necessary to paint the school in two days. Next painter was invited and all worked together. How long would this painter painted the school itself? - Two tributaries

Two tributaries of the pool fill it in 10 hours. One of the tributaries would fill 15 hours. How long would fill the first tributary? - Distance runner

Distance runner already climbed three fifths of the total route. Thus passed 90 km. How many km he have to stop? How long is his route? - Chimney

Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney. - Area of the cone

Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm. - Rectangles - sides

One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm^{2.}What are the dimensions of the original rectangle? - Teams

How many ways can divide 16 players into two teams of 8 member? - Quadratic equation

Determine the numbers b, c that the numbers x_{1}= -1 and x_{2}= 3 were roots of quadratic equation: ? - Apples

A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?

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