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

- Kuba,

- Two trains

Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak - Tractors

Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor? - Ages 2

A man's age is 4 times his son's age. After 5 years he will be just twice his son's age, find their ages. - The tub

If we drop the 5 l from the first tap and the from second 2 liters of water, the water in the tub will have a temperature of 25°C. If we drop 3 l from the first tap and from second 4 l of water, the water in the tub will have a temperature of 21°C. Determi - Two cities

The distance between cities A and B is 132 km. At 9.00 am, the cyclist started the bike at an average speed of 24 km/h, and at 10.00 h started from the B cyclist at an average speed of 30 km/h. How long and far from A will they both meet? - The pool

The pool contains 220 m^{3}of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B? - Mixing water

The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix? - Three unknowns

Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0 - Pooja

Pooja and Deepa age is 4:5, 4 years back it was 8:11. What is the age of Pooja now? - Beds

At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed? - Bucket

The bucket half filled with water weighs 5.55 kg, the full bucket weighs 9.85 kg. How much does the bucket weigh? - Pool

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? - TV transmitter

The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have. - Store

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. - Cuboid

Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm^{3}. Calculate the length of the other edges. - Right triangle Alef

The area of a right triangle is 294 cm^{2}, the hypotenuse is 35 cm long. Determine the lengths of the legs. - Circle arc

Circle segment has a circumference of 72.95 cm and 1386.14 cm^{2}area. Calculate the radius of the circle and size of central angle. - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}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.

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