Harmonic mean - practice problems - page 2 of 11
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: 207
- Pack of cream
A mother uses one pack of cream in 12 weeks, and a daughter uses it in 14 weeks. They used the cream together for four weeks, after which only the daughter used it. How many more weeks did the cream last? - Blueberries - total
Peter can fill a container with blueberries in 3 hours, and Jane in 2 hours. How long will it take them to fill the container together? - Instantaneous water heater
Water flows into and out of an instant water heater simultaneously. If water only flows in, the empty heater would be filled in 18 minutes. If water only flows out, the full heater would be emptied in 20 minutes. How many minutes will it take to fill the - Workers
The first worker can complete a job in 40 hours, the second in 50 hours, and the third in 80 hours. How long will it take them to complete the job if they all work together? - Princesses
Princesses Anna and Elsa are picking strawberries, which have ripened in huge quantities after a long winter. Anna can pick one bed in 120 minutes, and Elsa is faster and can finish an equally large bed in 15 minutes. How many minutes would it take the ro - Infinite speed
A runner completes her first lap of the track at an average speed of 5 km/h. How fast must she run her second lap so that her overall average speed for both laps is 10 km/h? - Decoration
Jerry and Jane decided to decorate their common room. If Jerry painted it alone, it would take her 4 hours, and Jane 3 hours. How long would they paint the room if they painted together? - Teacher paper correction
The new teacher corrects papers for 9 hours, and the older one fixes them in 6 hours. How much will they repair together? - Digger ditch together
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? - Company meadow mowing
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? - Open simultaneously
An empty tank is filled with inflow in 30 minutes. A full tank is emptied in 75 minutes with an open drain. How long does it take for an empty tank to fill up if both the inlet and outlet are open simultaneously? - Excavator pit days Two excavators dig a pit in 12 days. How much shorter will this job take if 8 excavators dig the hole? In 3 or 9 days?
- Potato harvesting
Due to a large potato harvest this year, the farm bought a new, more powerful sorter in addition to the old one. With both machines running simultaneously, the daily harvest is processed in 12 hours. If only the old machine were used, it would need 10 mor - Profit distribution workers
We have a profit of 40000e, and the work took 30 days. The first worker is promised 38% of the profit but only works for 15 days, the second worker is promised 33% of the profit and works for 20 days, and the third is promised 28% of the profit and works - Metro train increase
In the metro, trains run in one direction at the same speed and the same intervals. Yesterday, there were 24 trains throughout the day. More trains will run today, as the time interval between trains will be shorter by 20%. How many more trains will there - Together sewing
Eve sews a costume in 6 hours, Ivana in 8 hours, and Monica in 4 hours. How long will it take them to make the costume if they work together? - Basement pump water
After the flood, the Nováks would pump water out of the basement with one pump in 120 minutes, the second in 300 minutes, and the third in 600 minutes. How many minutes will it take them to pump the water out of the basement if they use all the pumps at o - Apartment cleaning together
A woman cleans an apartment in 8 hours and a man in 10 hours. How many hours will they clean together? - Tank inlet filling The tank is filled through three openings, A, B, and C. The simultaneously open inlets A and B are filled in 1 hour, inlets A and C in 45 minutes, and inlets B and C in 1.5 hours. How long would it take to fill each inlet separately?
- Vitamin doses
Children and adults take the recommended daily dose of vitamins throughout the year. According to the package insert, the recommended daily dose for a child is half that of an adult. Two adults together consume one pack of vitamins in 30 days. How many da
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