# Themes, topics - math word problems

1. Cyclist
Cyclist drives 5 km in half an hour, how long will drive in 3 hours?
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza and 45 for Petra. How long will it take to make records if they will work together?
3. Cook on gas
The gas cylinder will last for 30 weekends for 2 hours of daily cooking. How many days will we be able to cook on a new cylinder when we cook 3 hours a day?
4. Uphill and downhill
The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?
5. Gravitation
From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
6. Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
7. Rocket start
The body launched vertically up returns to the start site in 6 seconds. What height did it have?
8. Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
9. The work
The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take?
10. Athletic competition
In a 400 meter athletic competition, a participant covers the distance as given below. find the average speed? first 80 meters 10 m/s next 240 meters 7.5 m/s last 80 meters 10 m/s
11. Three people
Three people start doing a work at a same time. The first worked only 2 hours. The second ended 3 hours before the end. On an individual basis, it would take the first time to do the work 10 hours, second 12 hours and 15 hours third. How many hours did it
12. Four workers
Four workers will lay the floor of the gym in six hours. After an hour of working together, one of the workers left to the doctor. How long before the remaining three workers finish their work?
13. Eight hours
Brigadier Franta ties a sheaf of hay in 20 minutes. Lujza in the same time only a quarter. How many sheaves will they tie together in 8 hours?
14. Calories 2
Ben eats approximately 2400 calories per day. His wife Sarah eats 5/8 as much. How many calories does Sarah eat per day?
15. Lumberjacks
Fifteen lumberjacks would take 12 days to destroy the broken trees. How many days would this work require if 5 workers added to it after 4 days?
16. Luggage and air travel
Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lug
17. Ten cashiers
Ten cashiers are open at Tesco. Customers wait an average of 15 minutes. How many other cashiers have to open to reduce the waiting time by 4 minutes?
18. Flowerbed
Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
19. Inlet minus outlet
Water flows into the tank through two pipes and flows out of the third pipe spontaneously. The pipe A itself would fill the tank in 3 hours, the pipe B itself would fille in 4 hours, and the pipe C itself would flow out in 12 hours. How long will the tank
20. Candies
In the confectionery, the price for 1 kg of pistachio candies cost CZK 360, and the price for 1 kg of hazelnut candies was CZK 280. Mixing these two types of sweets created a box of chocolates. How many grams of pistachios and how many grams of hazelnut c

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