Harmonic mean - practice problems - page 9 of 10
The harmonic mean is a type of average that is particularly useful for calculating rates, ratios, or situations involving reciprocals.It is calculated as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers.
The harmonic mean is often used when dealing with averages of quantities like speed, where time and distance are inversely related. It tends to be less affected by extremely large values in a dataset, making it more appropriate for skewed distributions compared to the arithmetic mean.
A key property of the harmonic mean is that it is always less than or equal to the arithmetic mean and the geometric mean for any set of positive numbers.
It is commonly applied in finance, such as calculating the average price-to-earnings ratio, and in physics, such as finding equivalent resistance in parallel circuits. The harmonic mean is not suitable for datasets containing zero or negative values, as it is undefined in such cases.
Number of problems found: 186
- Pedestrian up-down hill
The pedestrian goes for a walk first on the plane at 4 km/h, then uphill at 3 km/h. Then it is in the middle of the route, turns back, and goes downhill at 6 km/h. The total walk was 6 hours. How many kilometers went pedestrians? - Garden
Father dug up the garden in 11 few hours. Son in 15 hours. How many hours does it take to dig up the garden together? - Fire tank
The whole fire tank was discharged once in 4 days, first out by a second in $n day. Once firefighters pumped out 4/16 of water from the tank, they let the water flow out both drains. How long does it take to empty the tank? - Painter Pavel
Painter Pavel painted the fence for 16 hours, and painter Petr painted the same fence for 13 h. How long should it take to paint the fence together?
- Three workers
Three workers, A, B, and C, must work on a specific task. Workers A and B completed the task in 22 days, B with C for 10 days, and A with C for 19 days. How long would it take to complete the task for everyone alone? How long would it take to complete the - Blueberries
Marie earns 3 liters of blueberries for 3.4 hours, and Peter 2.4 liters for 2.9 hours. How long do they pick one liter together? - Machines
There are three machines in the workshop. The first treats 250 parts for 4.7 hours, the second treats 300 parts for 1.9 hours, and the third treats 230 parts for 4.6 hours. How long will it take to make 3100 parts if all three machines are worked simultan - Two valves
Water fills the pool with two valves for 11 days. After 7 days, the workers stopped the first and second valve fill pool for 7 days. How many days did it take to fill the pool of each of the valves individually? - See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases.
- Average
What is the average speed of the car, where half of the distance covered passed at a speed of 52 km/h and the other half at 89 km/h? - Parquet floor
Three workers laid the parquet floor for 2.301 hour. The first would do this work alone 7 hours, the second in 6 hours. For how many hours would this work for the third worker if he worked alone? - Inflow - outflow
The tank will fill by inflow for 56 minutes and empties by outflow for 77 minutes. How long does it take to fill the tank if it is open to inflow and outflow? - Painters
The first painter painted the fence himself for 9 hours, the second painter 2.1 hours sooner than the first, and the third painter slowest up to 21 hours. How long took them to paint the fence if they worked together? - Workers
Two workers, A and B, will be done work together for 10 days. They worked together for 8 days. Then A worker became ill, and worker B finished the job alone for 6 days. If every worker worked alone, how many days did the whole work take for workers A and
- Madams
During spring cleaning, ladies were going to wash the windows. Mother takes 5 hours to wash all the windows, the grandmother takes 3 times longer, and Paula washes all the windows in 2 hours. How many hours will you spend washing the windows of this "wome - Car
The car goes from point A to point B at speed 84 km/h and back 67 km/h. If it goes there and back at speed 77 km/h trip would take 20 minutes shorter. What is the distance between points A and B? - Tanker
The first pump can empty an oil tanker in 4.9 hour, and the second pump can empty a tanker in 8 hours. If the first pump starts at 4:00 and the second starts 1.4 hour later, when will the tanker be empty? - Steamship
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? - Workers
Two workers would fulfill a certain task when working together for 10 days, the first if he worked himself done work in 17 days. How many days will the second worker do the whole job?
What is the reciprocal of the sum of the reciprocals of 7 and 6?Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
