Examples for 8th grade

Workers 2
Worker dug the trench for 7 hours, another worker for 10 hours. They recruited to work even one worker more. Digging should be done for 2 hours. For how long would dig third worker alone?
Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
Weights
Marry and John together weighing 49 kg. Their weights are in ratio 1:6. Determine their weights.
Two trains
Two trains go at each other. First at speed 40 km/h and the second at speed 60 km/h. At what distance will be 30 minutes before they will meet?
Chord 5
It is given circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle . Calculate its length.
Two looms
On two different looms with different performance can be make required quantity of textile in 6 hours when both work together. On the first machine this quantity of the textile can make in 10 hours. How long should take make same quantity of textile on a
Barrel 4
Barrel of water weighs 63 kg. After off 75% water, the weight of the barrel with water is 21 kg. How many kg weigh empty barrel and how many kgs water in it?
Savings and retirement
The older sibling has saved 44% more euros than the youngest, which represents 22 euros. How many euros older brother has saved ?
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?
Rectangle - sides 4
Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
Semicircle
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
Cubes
Most how many cubes with an edge length of 5 cm may fit in the cube with the inner edge of 0.4 m?
Truck PRG-BA
Truck driving on highway from Prague to Bratislava at average speed of 72 km/h. At the moment when the truck passes 54 kilometer from Prague passenger car departs from Prague which travel to Bratislava at speed 90 km/h. When and where (at waht highway k
Bronze, tin and copper
Bronze is an alloy of tin and copper. An alloy of 10% tin and 90% copper is Gunmetal. If it contains 20% tin and 80% copper, it is bell metal. How many tons of molten bell metal and how many tons of copper is needed to make 100 tons of Gunmetal?
Points on circle
In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are
Tree trunk
From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
Savings 2
Jozef and Michael saved 46 euros together. Michael saved 22 euros more than Jozef. How much did save each of them?
Brigade
On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week?
Diamond perimeter
Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm.

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