Harmonic mean - examples

  1. Two cyclists 2
    cyclist_45 At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,.
  2. Two cities
    cars_30 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?
  3. Two pumps together
    pumps_6 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?
  4. Water current speed.
    river_4 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.
  5. Pool
    pool If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
  6. Logic
    blue-barrel A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together?
  7. Tractors
    tractors Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors?
  8. Cyclist
    1cyclist Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
  9. Car
    american-cars Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B?
  10. Pedestrian up-down hill
    peak Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
  11. Workers
    two_workers Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days. If every worker was working alone, how many days took whole work for worker A and B?
  12. Workers
    workers Two workers fulfill a certain task when working together for 5 days, the first if he worked himself done work in 13 days. How many days will do whole job a second worker?
  13. Garden
    garden_2 Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together?
  14. Madams
    womans During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe
  15. Painter Pavel
    pixla_s_farbou Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
  16. Tanker
    oil-tanker An oil tanker can be emptied by the first pump in 4.9 hours. Second pump can empty an tanker in 8 hours. If the first pump started at 4:00 and second 1.4 hour later, at what time will the tanker be empty?
  17. Three workers
    three_workers Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 11 days, B together with C for 15 days, A together with C for 24 days. How long it would take to complete the task every one of them alone? How long it would.
  18. Steamship
    parnik Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h. What is the distance between the ports?
  19. Blueberries
    boruvky Marie earns 3 liters of blueberries for 3.4 hours, Peter 2.4 liters for 2.9 hours. How long have earns together one liter?
  20. Electronics: Resistors in parallel
    resistors_1 From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω

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