The most difficult problems
- Train speed
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is: - The diamond
The diamond has sides of 35 cm and the diagonals are in a ratio of 1: 2. Calculate the lengths of the diagonals. - Exponential warm
Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degree - Diagonal to area
Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Radioactive material
A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years? - Two chords
In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle. - Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Bitoo and Reena
Bitoo ate 3/5 part of an apple and the remaining part was eaten by his sister Reena. How much part of an apple did Renna eat? Who had the larger share? By how much? - Tallest and shortest
Jenn is the tallest on the team. He is 1 1/2 times as tall as the shortest girl whom is 4 1/4 feet tall. How tall is Jebb? - Twelve
Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each one students did in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by express - Raffle
There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together? - Rectangle area
The length of a rectangle of x units is increased by 10%, and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area of the new rectangle? - Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm³. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Scouts 4
4/7 of the students in a school are boys. If 3/8 of the boys are scouts, how many scouts are there in a school of 1878 students? - Two forces
The two forces F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F. - Borrowing
I borrow 25,000 to 6.9% p.a.. I pay 500 per month. How much will I pay and for how long? - Lemonade
How many 1/4 cup servings are in 2 and 1/3 cups of lemonade? - Clouds
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us? - The wall
The wall in the bathroom has dimensions of 2.8 m and 2.6 m. If we would like to cover this wall to a height of 1.6 m. How many square meters of tiles do we need to buy?
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