# Themes, topics - examples - page 16

1. Bob and Bobek
At 10h 20min runs Bobek from hat at average speed 12 km/h. At what time must run out Bob at speed 18 km/h to catch him 9 kilometers from the hat?
2. Bonbons 2
Kilo sweets will cost 260 CZK. The first type has a price per 320 kg, the second type 240 CZK per kg. How many kilos of both kinds of sweets need to prepare a 100 kg mixture ?
3. Concentration
How 0.5 liters of 8% vinegar diluted to a concentration of 20 hundredths % of vinegar? How many liters of water must be pour?
4. 5 pumps
Five pump to pump 3 hours 1600 hl of water. How long pumped same amount of water 4 pumps?
5. Square
Draw a square on the edge of a = 4 cm. Mark the center of symmetry S and all axes of symmetry. How many axes of symmetry does? Write down.
6. Alcohol 2
Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?
7. Average speed
What is the average speed you have to move the way around the world in 80 days? (Path along the equator, round to km/h).
8. Tank 9
The tank with volume V is filled with one pump for three hours and by second pump for 5 hours. When both pumps will run simultaneously calculate: a) how much of the total volume of the tank is filled in one hour b) for how long is the tank full
9. Painting school
Redecoration school had scheduled for four crew to 10 days. After two days a single worker ill. For how many days the school was painted when remain workers working with the same tempo?
10. Holiday SMS
Kucera and Malek start from the holiday together. They agreed that if they be 100 km apart, will send a SMS. Kucera traveling at 60 km/h., Malek 90 km/h. They started at 14 hours PM. At what time they send a message?
11. Master and apprentice
Master painted the roof in 3 hours and apprentice for 4 hours. How many of roof they painted in hour and how many in three quarters of an hour?
12. Alcohol mixing
How much 55% alcohol we must pour into 1500 g 80% alcohol to form a 60% alcohol? How much 60% alcohol created?
13. Workers 2
Worker dug the trench for 7 hours, another worker for 10 hours. They recruited to work even one worker more. Digging should be done for 2 hours. For how long would dig third worker alone?
14. On the farm
On the farm were housed 70 heads of cattle with food supply for 180 days. After 60 days, 10 head of cattle sold, and for the next 30 days they sold 10 more. How many days is sufficient supply of feed for the remaining cattle?
15. Hexagon = 8 parts
Divide the regular hexagon into eight equal parts.
16. Draw a trapezoid
Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
17. Salt
Sea water containing 5% salt. How many kg of fresh water necessary to pour into 40 kg of sea water so that the salinity fell to 2%?
18. Work at plant
Handyman has vowed to do repair work at the plant for 25 days. However, work had to be shortened and therefore gained helper. Together they made all the corrections for 13 1/3 days. How long the work would take helper himself?
19. Mason with assistant
Mason had to complete the work in 10 days. Two and a half days later his assistant arrived. Together they completed the work in next three and a half days. How many days would he need an assistant for the same work?
20. Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.