# Themes, topics - math word problems

1. Solutions, mixtures
How many liters of 70% solution we must add to 5 liters of 30% solution to give us a 60% solution?
2. Our house
Our house would paint four painters in 14 days. How long could it paint five painters? How long will it take if two other painters will come to help after 5 days?
What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
4. Workers
Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send?
5. Together
If 8 men, 10 women, 16 children collects ₹1024 in 4 days, how many days will be required for 6 men, 5 women and 4 boys to collect ₹768? (₹ is Indian Rupee)
6. Sand
The maximum weight of the car is 5000 kg. 10 m3 of sand must be transferred. How many times does a car have to go? (density of sand is 1500 kg/m3)
7. Triangles
Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have?
8. Three pumps
The water tank is emptied with the first pump in 6 hours, with the second pump in 2 hours. In order to be emptied in 1 hour, all three pumps had to be started at once. How long will take tank be emptied by only the third pump?
9. 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:
10. Thunderstorm
The sound travels 1 km in about 3 seconds. How far is the storm if there is a time interval of 8 seconds between lightning and thunder?
11. The bulbs
The bulbs are connected serially two bulbs and one resistor. Each bulb has a resistivity of 100 ohms and resistor of 60 ohms The voltage source in the circuit is 24 volts. Do you know what voltage to measure on individual appliances?
12. Map scale
The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
13. Painters
Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
14. Flying
The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
15. 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 degr
16. Electric energy
There are 875 identical light bulbs in the sports hall lighting for 2 hours. How long does the same amount of electricity consume 100 such bulbs?
17. Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
18. Fruit juice
Fruit juice contains 37.5% sugar. How many percents of sugar will be in the flavored mineral that we prepare from 100 grams of fruit juice and 1.4 liters of mineral? (1 liter = 1 kg)
19. Construct
Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
20. Five pumps
The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps?

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