Themes, topics - examples
- The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r
- Six-digit primes
Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
- Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
- The cyclist
The cyclist drove from A to B, 60 km away. The first half drove at 30km/h, the second at 20km/h. How long did it take for him?
- Vinegar mixing
We mix 70g water and 50g 8% vinegar. How many percents of the solution of vinegar we produce?
- 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
Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
- Three machines
The power of the three machines is 2: 3: 5. Two most powerful machines produce 400 parts per hour. How many components make all three machines in 3 hours?
Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor?
- Water current speed.
Two cities along the river are 100 km apart. The powerboat downstream runs for 4 hours, upstream for 10 hours. Determines the river's current speed.
- Three pumps
We are filling the pool. The first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump?
- Two cities
The distance between cities A and B is 132 km. At 9.00 am, the cyclist started the bike at an average speed of 24 km/h, and at 10.00 h started from the B cyclist at an average speed of 30 km/h. How long and far from A will they both meet?
- The pool
The pool contains 220 m3 of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B?
- Two vans
At 8:30 a. M. , two vans leave at a parking area. They travel in opposite directions: one van travels at 48 km/h and the other at 62 km/h. At what time will the cars be 550 km apart?
- Express train
International express train drove from Kosice to Teplice. In the first 279 km, the track was repaired, and therefore it was moving at a speed of 10km/h less than it was scheduled to drive. The rest of the 465 km trip has increased the speed by 8 km/h than.
- Mixing water
The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix?
- Orlík hydroelectric plant
The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the p
- Effective and mean voltage
A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source, R2 is connected to a voltmeter which measures the mean voltage and has an internal resistance R3 = 200300 Ω, the measured value is
Lucie can walk about 3 4/5 miles each hour. How far can she walk in 2 hours 45 minutes?
- Working together
One worker performs work in 3 days, the second in 5 days. How much do they work together?