# 8th grade (13y) + system of equations - examples

- Father and daughter

When I was 11 my father was 35 year old. Now, father has three times older then me. How old is she? - 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. - Pool

If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately? - 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? - Coffee

In stock are three kinds of branded coffee prices: I. kind......248 Kč/kg II. kind......134 Kč/kg III. kind.....270 Kč/kg Mixing these three species in the ratio 10:7:7 create a mixture. What will be the price of 1100 grams of this mixture? - 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? - 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. - Chickens and rabbits

In the yard were chickens and rabbits. They had 28 heads and 82 legs. How many chickens and how many rabbits was in the yard? - 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. - 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? - 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. - Barrel of oil

Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel? - 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 - 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? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 21 cm and t_{b}=12 cm.

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