8th grade (13y) + system of equations - examples
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
- Forestry workers
In the forest is employed 43 laborers planting trees in nurseries. For 6 hour work day would end job in 35 days. After 11 days, 8 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da
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?
In stock are three kinds of branded coffee prices: I. kind......6.9 USD/kg II. kind......8.1 USD/kg III. kind.....10 USD/kg Mixing these three species in the ratio 8:6:3 create a mixture. What will be the price of 1100 grams of this mixture?
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.
If you go at speed 5.1 km/h, you come to the station 37 minutes after leaving train. If you go by bike to the station at speed 28 km/h, you come to the station 38 minutes before its departure. How far is the train station?
- Right triangle Alef
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
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?
- Chickens and rabbits
In the yard were chickens and rabbits. They had 31 heads and 94 legs. How many chickens and how many rabbits was in the yard?
- Circle arc
Circle segment has a circumference of 41.89 m and 251.33 m2 area. Calculate the radius of the circle and size of central angle.
- Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
- Right triangle
Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
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
- Barrel of oil
Barrel of oil weighs 253 kg. When it mold 43% oil, weighed 159 kg. What is the mass of the empty barrel?
- Rectangle - sides ratio
Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
- Pedestrian up-down hill
Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
- The cyclist
The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town.
Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days. If every worker was working alone, how many days took whole work for worker A and B?