# Rational numbers - problems

1. Bonus
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
2. Troops
Route is long 147 km and the first day first regiment went at an average speed 12 km/h and journey back 21 km/h. The second day went second regiment same route at an average speed 22 km/h there and back. Which regiment will take route longer?
3. 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?
4. 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?
5. Logic
A man can drink a barrel of water for 26 days, woman for 48 days. How many days will a barrel last between them?
6. Beer
After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
7. 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
8. Coffee
In stock are three kinds of branded coffee prices: I. kind......248 Kč/kg II. kind......134 Kč/kg III. kind.....270 Kč/kg Mixing these three species in the ratio 10:7:7 create a mixture. What will be the price of 1100 grams of this mixture?
9. 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?
10. Store
One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
11. 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
12. 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.
13. River
Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
14. 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.
15. Server
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
16. Pool
The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
17. Discount
Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 70 USD. Determine the original price of sweater.
18. Scale
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
19. 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?
20. 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 €.

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