Theme - problems
- Sea water
Seawater contains about 7% salt. How many dm3 of distilled water we must pour into 14 dm3 of sea water to get water with 1.7% salt?
- Sea water
Mixing 68 kg of sea water with 73 kg rainwater is created water containing 3% salt. How many percent sea water contains salt?
- Pedestrian up-down hill
Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car.
- Parquet floor
Three workers laid parquet floor for 1.957 hour. The first one would do this work alone 5 hours, the second in 9 hours. For how many hours would fulfill this work the third worker, if he worked alone?
- Christmas Day
In leap years was 53 Sundays. On what day of the week fell to Christmas Day?
- Reservoir + water
Reservoir completely filled with water weighs 13 kg. After pouring off three quarters of the amount of water weights 4 kg. Calculate the weight and volume of the reservoir.
76% acid was make from same acid of two different concentrations. Amount weaker acid to the stronger acid is in ratio 2:1. What was the concentration of the weaker acid, if stronger had 94% concentration?
- Two workers
The first worker completed the task by himself in 9 hours, the second in 18 hours. After two hours of joint work left first worker to a doctor and the second finished the job himself. How many hours worked second worker himself?
- Train from Prague
First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
- Two runners
Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute
- Fire tank
Whole fire tank was discharged once in 2 days by first out by second in $n days. Once firefighters pumped out 1/9 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to.
- Warehouse cars
From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck?
The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries?
Ball was fired at an angle of 33° at initial velocity 419 m/s. Determine the length of the litter. (g = 9.81 m/s2).
- Ascent and descent
Car goes 114 km track, which consists of ascent and descent at time of 1 hour 35 minutes. When climbing moves at the speed 48 km/h and downhill 25 m/s. What is the length of climb and descent?
- Cars motion
From point A car start at the speed of 90 km/h. Against it departs from the point B at the same time another car at 60 km/h. For how long and where they met if the distance between A and B is 180 km?
- Three points
Mark three points E, F and G in the plane not lie on one line. a) Draw a line segment FG b) Construct halfline (ray) EG c) Draw a line EF
Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any