# Themes, topics - math word problems

1. Journey 5 A man has to do a journey of 84km in 3 hours. He travels the first 30km at 20km/hr. At what rate must he travel the remaining distance to complete his journey on time?
2. Two pipes How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
3. Two airports Two airports are 2690 km away. From the first airport, the airplane flies at a speed of 600 km/h, from a second airplane at a speed of 780 km/h. When will they meet if they flew at 10:00? How far from the first airport?
4. Two cities The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
5. Iron density Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
6. Two pumps together The first pump will fill the tank itself in 3 hours and the second one in 6 hours. How many hours will the tank be full if both pumps are worked at the same time?
7. 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?
8. Clogging How much distilled water must the pharmacist add to 30g of a 30% hydrogen peroxide solution to obtain a 3% solution to clogging?
9. 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?
10. 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.
11. Vinegar mixing We mix 70g water and 50g 8% vinegar. How many percents of the solution of vinegar we produce?
12. 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
13. Mushrooms Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
14. 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 ta
15. 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?
16. Tractors 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?
17. 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.
18. 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?
19. 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?
20. 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?

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