# Algebra - math word problems

- Three lines

At 6 am, three bus lines are departing from the station. The first line has an interval of 24 minutes. The second line has an interval of 15 minutes. The third line runs at regular intervals of more than 1 minute. The third line runs at the same time as t - Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Before yesterday

He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the - A rhombus

A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - Positional energy

What velocity in km/h must a body weighing 60 kg have for its kinetic energy to be the same as its positional energy at the height 50 m? - Isosceles triangle 10

In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles. - The hemisphere

The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - A concrete pedestal

A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal. - Floating of wood - Archimedes law

What will be the volume of the floating part of a wooden (balsa) block with a density of 200 kg/m3 and a volume of 0.02 m^{3}that floats in alcohol? (alcohol density is 789 kg/m3) - AM of three numbers

The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers. - Common divisors

Find all common divisors of numbers 30 and 45. - Frustum of a cone

A reservoir contains 28.54 m^{3}of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone. - Alcohol

6l 48% alcohol, how much 52% alcohol must be added to give 50% alcohol? - Cylinder and its circumference

If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c? - Reducing balance method

A company buys an item having a useful life of 10 years for 1,000,000. If the company depreciates the item by the reducing balance method, a. Determine the depreciation for the first year. b. Estimate the depreciation for the second and third years. c. - Surface of the cylinder

Calculate the surface of the cylinder for which the shell area is Spl = 20 cm^{2}and the height v = 3.5 cm - Cuboid face diagonals

The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - Body diagonal

Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm - Simple equation 10

35= 7*3*x what is x? - The escalator

I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I clim

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