# Algebra - problems - page 84

1. The tourist
The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
2. The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
3. Equation
Find x: x + 1/2 = 1/3
4. Two workers
The first worker would himself completed the work in 8 hours, the other in 6 hours. After two hours of joint work left the first worker to a doctor and other completed work himself. How many hours worked the other worker himself?
5. Viju
viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with viju??
6. Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
7. Inscribed circle
Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
8. Work
The first worker would need less than 4 hours to complete the task than the other worker. In fact, both workers worked for two hours together, then the first worker did the remaining work himself. In what proportion should the remuneration of the workers b
9. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
10. Cube surface and volume
Find the surface of the cube with a volume of 27 dm3.
11. The tank
The tank had 9 inflows to be filled in 21 days. After 9 days, 3 trips out. How many days did the remaining 6 tributaries fill the tank?
12. Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
13. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
14. Savings
Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
15. Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
16. Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
17. MO C–I–1 2018
An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
18. 7 digit number
If 3c54d10 is divisible by 330, what is the sum of c and d?
19. Flowerbed
Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
20. The painter
In order for the painter to get the desired color, he must mix green and yellow in a ratio of 4: 7. If it has 28 l of green color, how many liters of yellow color should he add? How many liters of mixed color does he get?

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