Examples for 8th grade - page 97
- Two workers
Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself?
- Parcel 4
To send a parcel by messenger within city limits costs 60 cents for the first pound and 48 cents for each additional pound. What is the cost, in cents, of sending a parcel weighing p=4 pounds?
- Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
- Interior designer
To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?
- Stones in aquarium
In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
Grandfather, father, and son are carpenters. They decided to make a wardrobe. Father produces it for 12 hours, his son for 15 hours, and grandfather for 10 hours. How long will they make it together?
Two turners perform joint work in 3 hours. The first turner would perform the job himself in 7 hours. How long would the same job last for a second turner if he worked alone?
Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
When a bricklayer works himself to redeem the house in 8 days, the other bricklayer will be finished in 10 days. How long will it take to make 3 such houses together?
- Two pumps
Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself?
Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
- ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
- Find the
Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
- In and out
The empty tank is filled in 12 minutes and empty in 16 minutes. How long does it take to fill if we forgot to close the drain? If the tank has 1000 l.
- Vehicle tank
A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold?
Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together?
- Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They
Six seamstresses should make 60 shirts in five business days. After three days two seamstresses were sick. How many days have the remaining seamstresses to finish contract?
- Angle of diagonal
Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
- Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.