# Units - examples - page 38

1. Solution
In 469 dl red solution is 84 dl red color and in 102 dl blue solution is 52 dl blue color. How many dl of red and blue dl color solution must be mixed to get a mixture of 247 dl contain 116 dl of color?
2. Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
3. Painting rooms
If Dano paint three hours daily given work he complete in 7.5 days. How many hours a day would have to work to finish the job 1.5 days earlier?
4. Father and son
Father is 48 years old, son 23. When will be the father twice older than a son?
5. Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
6. Walkers
From points A and B simultaneously started against each other two walkers. After meeting both continue to B. Second walker came to B 2 hours before the first walker. It's speed is 2.7 times of speed of the first pedestrian. How many hours went pedestria
7. Tractors
Uncle is going buy tractor Zetor super 50. The first costs 81000 Eur, the second costs 98000 Eur. How much pay uncle for both tractors?
8. Landlord
Landlord had 49 ducats more than Jurošík. How many ducats Jurošík steal landlord if the Jurošík now 5 ducats more?
9. 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.
10. Copiers
The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
11. Angles and sides of the triangle
Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
13. Homework - jumps
Sasha jumped 121 cm Peter 4 cm more than Jirka. Jirka 6 cm less than Misha. Misha 7 cm less than Filip and Filip half as much Sasha and Petr together. How far each jumped?
14. Tachometer
Tatra's tachometer shows the initial state 886123 km this morning. Tatra today travel at an average speed of 44 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4 hours?
15. Sphere area
A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
16. Arc
Convert to arc measures (radians): 924 ° Result write as a multiple of π
17. Workhorses
A team of colleagues done the work in 20 days. After adding 2 colleagues from the beginning the work was completed in 15 days. How many members has the colleague team?
18. Cylinder surface, volume
The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of cylinder.
19. TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the minutes of the actual program. Determine how many minutes of the program are shown in that one hour.
20. Rope
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?

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