Reason + real numbers - practice problems
Number of problems found: 16
- Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than the second one. How many minutes is filled with the first pump? - Pump
What power does a pump output to move 4853 hl of water to a height of 31 m for 8 hours? - Real estate
The residential house has three entrances numbered by odd numbers arithmetic progression. The sum of the two numbers on the corner entrances is 50. Calculate the highest of these three numbers. - Possibilities 5590
The line represents the number axis, and the marked points correspond to the numbers a, - a, and + 1, but in no particular order. Construct the points that correspond to the numbers 0 and 1. Discuss all the possibilities. - 2x cone
Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone. - Inequality 7320
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - Discounts on rail (ZSSK)
The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week. - Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Aircraft
Flight length 3457 km took 5 hours. The airport passengers had to arrive hours in advance, 2 hours. Departure was delayed for 6.4 hours. The destination airport formalities took 0.4 hours. Calculate the average speed of passenger travel from arrival to le - Garden
The square garden area is 2/9 of triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing need to fence a square garden? - Gutter
How much metal is needed to produce 60 pieces of gutter pipes with the diameter 17 cm and length of 6 m? The plate bends add 6% of the material. - When will I be a millionaire?
Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures are ignored. - Forestry workers
56 laborers have employed planted trees in the forest. For 8 hour work, a day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others if they work 10 hours a day? - Youth track
Youth track from Hronská Dúbrava to Banská Štiavnica, which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate the size of subsidies to a trip group - Rajendra
Rajendra, a farmer, had two sons and two daughters. He decided to divide his property among his sons and daughters. So he wrote a "WILL" about the distribution of his property. According to his "WILL," he desired to give 3/5 of the property to his sons in - Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately?
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