System of equations - problems

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  1. Motion
    cycling Cyclist started at 5:00 from point N to point O. After 20 minutes, followed him at the same speed the second cyclist. Walker, which went from O to N, started at 5:40. After 56 minutes he met the first cyclist and after next 16 minutes the second cyclist. D
  2. Gear
    ozubene_kolesa Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?
  3. Right triangle
    righttriangle Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle.
  4. Ships
    titanic_1 At 15:20 the ship set sail at 16 km/h. At 17:50 followed by at 41 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took?
  5. RT - hypotenuse and altitude
    pravy_trojuholnik Right triangle TWS has hypotenuse s=202 km and altitude to s is 99 km. How long are hypotenuse segments?
  6. Barrel 3
    sud-s-vodou Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
  7. Euler problem
    euler Someone buys a 720 tolars towels. If it was for the same money of 6 more towels, it would be 6 tolars cheaper each. How many were towels?
  8. Pharmacy
    lekarna At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 24 L of 36-percent solution. What amount of solution from each container is needed to mix?
  9. Geometric sequence 3
    sequence In geometric sequence is a6 = 77760; a7= 466560; sn=93310. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
  10. Angles in triangle
    trigonometry The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle?
  11. Angles in a triangle
    fun The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=69°. What sizes have other angles in a triangle?
  12. Honza + Alice + Tonda
    minca Honza + Alice + Tonda have a total of 1480 USD. The ratio between Honza and Alena is 5:6 and the ratio between Alice and Tonda is 4:5 How many money have each of them?
  13. Vacation
    motion Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When grand
  14. Bases
    trapezoids_1 The length of the bases trapezium are in ratio 2:1. Length of midline is 17. How long are the bases of a trapezoid?
  15. Null points
    absolute value Calculate the roots of the equation: ?
  16. Playing Cards
    cards_1 Kara has 4 times more cards than Dana, Dana has 6× less than Mary. Together they have 649 cards. How many cards has each of them?
  17. Jane and Miro
    two_men Jane brother Miro is 42 years. And he is three times old as it was Jane when Miro was for so many years as there are now Jane. How old is Jane?
  18. Alfa, beta, gama
    angles_in_triangle In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
  19. Borrowed book
    TB Jane must as soon as possible return a borrowed book. She figured that when she read 15 pages a day return book in time. Then she read 18 pages a day and then return the book one day before. How many pages should have a book?
  20. Alcohol mixing
    lieh How much 55% alcohol we must pour into 1500 g 80% alcohol to form a 60% alcohol? How much 60% alcohol created?

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