Examples for 8th grade

Two trains meet
From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B is 386 1/4 km. At what time and at what distance from B the two trains meet?
Passenger car and truck
From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck?
Combinations of sweaters
I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
Boots
Master shoemaker has three apprentices. First do one pair of boots for two days, second for 1 day, third on 1.5 day. If they worked together, for how long it would take made a couple of boots?
Rhombus
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
Banknotes
$ 1390 was collected. How much was in $20 notes and how many in $50 notes in that order? How many solutions exists?
Cat
One-fifth of the monthly pocket money contributes Maros for food for his cat, half of the rest postpone for a new smartphone. The remaining € 8 spend. How much pocket money gets Maros a month?
Cyclist
Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?
Outer contact of circles
Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S₁S₂S₃.
Shoes and slippers
Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers?
Trucks
Truck take you the some amount of clay in 30 hours. Second truck in 40 hours. Trucks carted the clay away some time together then the second truck broke down and the first one completed the job in five hours. What time worked together?
Welders
Welder do the job for six hours, the second one for 8 hours. How long do the job third welder if all together can do job in 2 hours?
Three ints
The sum of three consecutive integers is 2016. What numbers are they?
Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
Hexagon area
The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
Tent
Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
Circle chord
Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.
Kite
John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending.
Windbreak
A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
Embankment
Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.

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