# Examples for 8th grade - page 96

1. Repair pipe
20 workers had to repair broken pipes in 30 days. After fourteen days, four laborers joined them. How long did the pipe repair work last?
2. Five pumps
Three same pumps fill the tank with 50400 liters of diesel in 7 hours. How many liters of diesel will it take in 4 hours if we add two more of the same pumps and pump them the same way? How much more (or less) will they get if we add 2 of the same pumps a
3. Land area
A land area of Asia and Africa are in a 3: 2 ratio, the European and African are is 1:3. What are the proportions of Asia, Africa, and Europe?
4. Working together
One worker performs work in 3 days, the second in 5 days. How much do they work together?
5. Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
6. Apples
School kitchen bought 36kg apples for 12 kc/kg. How many kilograms of apples 1/4 cheaper can they buy for the same money?
7. Isosceles
Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
8. Mail train
The speed of mail train is 1370 meter per minute. Express it in miles per hour correct to three significant figure . Given that 1 meter =39.37 inches.
9. Angle of diagonal
Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
10. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
11. Stones in aquarium
In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
12. Two pumps
Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself?
13. Four workers
Four workers will lay the floor of the gym in six hours. After an hour of working together, one of the workers left to the doctor. How long before the remaining three workers finish their work?
14. Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
15. Turners
Two turners perform joint work in 3 hours. The first turner would perform the job himself in 7 hours. How long would the same job last for a second turner if he worked alone?
16. The work
The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take?
17. ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
18. Bricklayers
When a bricklayer works himself to redeem the house in 8 days, the other bricklayer will be finished in 10 days. How long will it take to make 3 such houses together?
19. Triangles
Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?
20. Performance
Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together?

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