# Equation - high school - examples

- Two cyclists 2

At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,. - Journey 5

A man has to do a journey of 84km in 3 hours. He travels the first 30km at 20km/hr. At what rate must he travel the remaining distance to complete his journey on time? - Mushrooms

Grandfather gathered fresh mushrooms. The fifth was wormwood, and it was thrown away, the other dried up. He obtained 720 grams of dried mushrooms. How many kilograms did the grandfather collect, and by drying the mushrooms they lost 75% of their weight? - Two pipes

How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time? - Two cities

The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B? - Employees

There are 1116 people working in three factory halls. In the first one, there are 18% more than the third, and 60 persons more than the second. How many employees work in individual halls? - Clogging

How much distilled water must the pharmacist add to 30g of a 30% hydrogen peroxide solution to obtain a 3% solution to clogging? - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm^{2}and side is 13 cm long. - Three friends

Cuba, Matthew and their friend Adam found a brigade during their weekend weekends because they wanted to make a joint trip to the Alps that they planned for the spring break. Cuba enjoyed the skiing trip very much, so he was not lazy to get up and went t - Two trains

Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak - Substitution method

Solve goniometric equation: sin^{4}θ - 1/cos^{2}θ=cos^{2}θ - 2 - Diagonals of a rhombus 2

One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm^{2}, find the side of the rhombus. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - 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? - Bonus

Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses? - Logic

A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together? - Beer

After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille? - Clock

How many times a day hands on a clock overlap? - Server

Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%. - River

From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.

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