# 9th grade (14y) + system of equations - examples

- Pool

If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately? - Store

One meter of the textile were discounted by 2.4 USD. Now 6 m of textile cost as before 3 m. Calculate the old and new price of 1 m of the textile. - Cuboid

Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm^{3.}Calculate the length of the other edges. - Right triangle Alef

The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs. - Circle arc

Circle segment has a circumference of 13.26 mm and 252.03 mm^{2}area. Calculate the radius of the circle and size of central angle. - Triangle ABC

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19 - Motion

Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D - Right triangle

Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle. - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - R triangle

Calculate the area of a right triangle whose longer leg is 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg. - Barrel of oil

Barrel of oil weighs 238 kg. When it mold 20% oil, weighed 196 kg. What is the mass of the empty barrel? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm. - Rectangle - sides ratio

Calculate area of rectangle whose sides are in ratio 1:7 and perimeter is 735. - The cyclist

The cyclist went from village to town. First half of journey went at 19 km/h. The second half of the journey, which mostly fell, went at 33 km/h. All journey took 67 minutes. Calculate the distance from the village to the town. - Workers

Workers A and B will done work together for 20 days. They worked together 18 days. Then A worker became ill and worker B finish the job alone for 11 days. If every worker was working alone, how many days took whole work for worker A and B? - Ships

At 15:20 the ship set sail at 16 km/h. At 17:50 followed by at 41 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took? - Team

The football team has 11 players. Their average age is 21 years. During the match due to injury, one player withdraws and the average age of the team is 20. How old was injured player? - Tourists

From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 39 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group? - 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? - Freedom

In the city are 2/6 of women married for 4/4 men. What proportion of the townspeople is free (not married)? Express as a decimal number.

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