# 6th grade (11y) + rational numbers - examples

1. Motion problem
From Levíc to Košíc go car at speed 81 km/h. From Košíc to Levíc go another car at speed 69 km/h. How many minutes before the meeting will be cars 27 km away?
2. Excavation
Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
3. Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth l
4. Motion
If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure. How far is the train station?
5. Medicament
Same type of medicament produces a number of manufacturers in a variety of packages with different content of active substance. Pack 1: includes 60 pills of 600 mg of active substance per pack cost 9 Eur. Pack 2: includes 150 pills of 500 mg of active sub
6. Hands
The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
7. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
8. Motion2
Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
9. ŽSR
Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 4-shift operation. Consider the average salary of the employee 885 €.
10. School trip
School trip cost 247.2 Eur for one class (24 students). How much would cost a trip for two classes? (both classes together have 53 students)
11. Youth track
Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate size of subsidies to trip group of 28.
12. Compare
Compare fractions ?. Which fraction of the lower?
13. Rainfall
Annual rainfall in our country are an average of 797 mm. How many m3 of water rains on average per hectare?
14. Alcohol
How many 55% alcohol we need to pour into 14 liters 75% alcohol to get p3% of the alcohol? How many 65% alcohol we get?
15. Ravens
The tale of the Seven Ravens were seven brothers, each of whom was born exactly 2.5 years after the previous one. When the eldest of the brothers was 2-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur
16. Time
Write time in minutes rounded to one decimal place: 5 h 28 m 26 s.
17. Camp
In the camp are children. 1/2 went on a trip, 1/4 went to bathe and 38 children remained in the room. How many children are in camp?
18. Bricks
Brick has volume 2.2 dm3. How many bricks can drive truck with capacity 23 ton? The density of brick is 1.6 g/cm3.
19. Sea water
Mixing 34 kg of sea water with 34 kg rainwater is created water containing 3.4% salt. How many percent sea water contains salt?
20. One sixth
How many sixths are two thirds?

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