# Examples for 9th grade - page 30

- Mother and daughter

Three years ago mother was three times older than daughter. After nine years she will be only twice old. How old is mother (and daughter)? - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance? - Work

First paver pave pavement for 33 hours. Second for 24 hours. Started first paver and after 5 hours, join the second. How long will they finish pavement? - Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth. - Cross-country competition

Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B? - Triangle

Calculate the area of the triangle ABC if b = c = 20 cm, R = 21 cm (R is the circumradius). - Gasholder

The gasholder has spherical shape with a diameter 23 m. How many m^{3}can hold in? - Cuboids in cube

How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters? - Elections

In elections candidate 8 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes. - Exam average

Average of marks that have on the certificates students of 8.A class in mathematics is exactly 2.45. If we did not add 1 and 3 of sutdents Michael and Alena, who arrived a month ago, it would average exactly 2.5. Determine how many students have class 8. - Workman - shift

The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components? - Bath

In the bath is 30 liters of hot water. Then added 38 liters of cold water at temperature of 17 °C decreased temperature of water to 48 °C. What was the initial temperature of the hot water? - Warehouse cars

From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck? - Tunnels

Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any - Paul and Honza

Honza went to chat on a bike without a break 3.0 hours. Paul the same way without breaks 30 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not. - Chess

How many ways can select 3 fields on classic chess board with 64 fields, so that fields don't has the same color? - Painters

First painter painted fence himself for 12 hours, the second painter 3 hours sooner than first, and the third painters slowest up to 20 hours. How long took them paint fence if worked together? - Four-digit number

Find also a four-digit number, which quadrupled written backwards is the same number. - Katy MO

Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY? - Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.

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