Harmonic mean - practice problems
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: 187
- Two masons
Mason A can build a wall in 30 days, while mason B can build it in 40 days. If they build it together and get a payment of USD 7000, what is B's share? - Avg velocity
A car travels 120 km at 60 km/hr and another 120 km at 40 km/hr. What is its average speed? - Four legs of journey
A car driver covers a distance between two cities at a speed of 60 kmph and on the return, his speed is 40 kmph. He goes again from the first to the second city at twice the original speed and returns at half the original return speed. Find his average sp - Avg speed 2
A car covers four successive 3 km stretches at 10 kmph, 20 kmph, 30 kmph, and 60 kmph, respectively. What is the average speed over this distance?
- A train 5
A train travels from Brno to Ass at a speed of 45 km/h and returns back at a speed of 36 km/h. Find the average speed of the train. - One-third 18
One-third of a certain journey was covered at the speed of 20 km/h, one-fourth at 30 km/h, and the rest at the speed of 50 km/h. Find the average speed of the whole journey. - Automobil The car traveled three quarters of the total journey at a speed of 90 km/h and the remaining part of the journey at a speed of 50 km/h. Find its average speed.
- Three workers
Three people - A, B, C . A and B can do a piece of work in 18 days, B and C can do it in 24 days, A and C can do it in 36 days.In how many days B alone can finish the work? - Rasmus Rasmus goes from station A to station B at the speed of 40km/h and returns B to A at the speed of 60 km/h. Find his average speed.
- One hour
If a pipe can fill a tank in 5 h and another pipe can empty the tank in 10 h, if both pipes are opened simultaneously, how many parts are filled in 1 hour? - Three pipes PPM
Pipe A can fill a tank in 20 h while pipe B can fill it in 10 h and pipe C can empty the full tank in 30 h. If all the pipes are opened together, how much time will be needed to make the tank full? - Two men
2 men or 3 women can do a piece of work in 45 days. Find, in how many days 6 men and 1 women be able to complete the same work. - A piece of work
12 men or 18 women can do a piece of work in 14 days, then how long 8 men and 16 women take to finish the work? - A boat
A boat covers 20 km in an hour downstream and covers the same distance in 2 hours upstream. Then, find the speed of the boat in still water and the speed of the stream.
- Three journeys
If a person covers three equal distances at the speed of 30 km/h, 15 km/h and 10 km/h respectively, then find out the average speed during the whole journey. - Mean proportional
What will be the mean proportion between 4 and 25? - Decoration
Jarka and Jana decided to decorate their common room. If Jarka painted it alone, it would take her 4 hours, and Jane 3 hours. How long would they paint the room if they painted together? - Corrects 83017
The new teacher corrects papers for 9 hours, and the older one fixes them in 6 hours. How much will they repair together? - Together 82965
An older digger would dig a ditch by himself in 6 hours. A younger digger can handle the same trench in 3 hours. How long would it take them to dig if they worked together?
The K+S company will mow the meadow in ten hours. The Kosačka company mows the meadow in six hours. How many hours would these companies mow one such meadow if they worked together?Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
