# 6th grade (11y) + system of equations - examples

- Forestry workers

In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da - 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? - 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? - 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? - Two squares

Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares. - Chamber

In the chamber light is broken and all from it must be taken at random. Socks have four different colors. If you want to be sure of pulling at least two white socks, we have to bring them out 28 from the chamber. In order to have such certainty for the pai - Gear

Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears? - Motion

Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di - Cents

Julka has 3 cents more than Hugo. Together they have 27 cents. How many cents has Julka and how many Hugo? - Lentilka

Lentilka made 31 pancakes. 8 don't fill with anything, 14 pancakes filled with strawberry jam, 16 filled with cream cheese. a) How many Lentilka did strawberry-cream cheese pancakes? Maksik ate 4 of strawberry-cream cheese and all pure strawberry pancake - Ratio

6 numbers are in the ratio 1:5:1:5:5:5. Their sum is 242. What are the numbers? - Rabbits

In the hutch are 48 mottled rabbits. Brown are 23 less than mottled and white are 8-times less than mottled. How many rabbits are in the hutch? - Trio

Trio of workers earn 750 euros. Money divided by the work that each of them made. First received twice as the second, the second received three times more than the third. How many got everyone from workers? - Father and son

Father and son are together 80 years. Son is 28 years younger than father. How old is the son? - Truck

Truck went for 4 hours and 48 minutes. If truck increase speed by 21 km/h, went same distance in 1.8 hours. Calculate this distance. - Paddlers

Students of canoeists trip traveled in three days 102 km. Second day traveled 15% more than first day and at the third day 9 km over the second day. How many kilometers traveled each day? - Gardens

The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens? - Family and age ratios

Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother? - Family

Martin has just as brothers as sisters. His sister Jana but has 2 times more brothers than sisters. a) How many children are in this family? b) How many boys and how many girls are in the family? - Warehouses

To four warehouses is going cement in 25 kg bags. To first one third, to second quarter of the total. The third store got two thirds of the rest, and the last 310 tons came to fourth. How many cement is in all warehouses and how much got every one?

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