Harmonic mean - practice problems - page 5 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
- Triangle 8320
Is there a triangle with heights of 4, 7, and 10 meters? - Reading records
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza, and 45 for Petra. How long will it take to make records if they will work together? - Uphill and downhill
The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist? - Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to the done work in 12 days?
- Athletic competition
In a 400-meter athletic competition, a participant covers the distance given below. Find the average speed. first 80 meters 10 m/s next 240 meters 7.5 m/s last 80 meters 10 m/s - Carpenters
Carpenters 1 and 2 spend ten days and five days, respectively, to make one table. The first carpenter and 30 made 50 tables by the second. What is the average time spent on the products? - Minutes 8081
I will drain the whole tub in 4 minutes. How long would it take to drain it if I added two more drain holes? - Ten cashiers
Ten cashiers are open at Tesco. Customers wait an average of 15 minutes. How many other cashiers have to open to reduce the waiting time by 4 minutes? - Flowerbed
Ondra digs the bed in 20 minutes, Cuba in 30 minutes. How long do they dig together?
- Two cyclists 2 At the same time, two cyclists left towns A and B at constant speeds. The first one goes from town A to town B, and the second one from town B to town A. At one point during the trip, they met. After they met, the first cyclist arrived at town B in 36min,
- Construction 7709
Two construction companies are working on the landscaping. The first would do the whole job in 12 days, the second in 20 days. How long will they work together if the first start working when the second has already worked 4 days? - Kilometers 7684
My father went to dig 6 kilometers of beet at 6:00 pm. It would take him 12 hours. After an hour, the son arrived, and they finished digging at 10:00. How long would it take for his son to dig 6 km of beet? - Identical 7683
In a hotel pool, the pool manager drains the water through two identical drains every 10 hours. How much time would he save in draining the pool if the water was drained through three more drains at the same flow rate? - Tributaries 7678
We filled the pool with two tributaries: the first in 5 hours and the second in 8 hours. The father came and drained 1/8 of the water. How long before the pool fills with both tributaries?
- Kilometers 7631 At 8:00, Peter set out on a hike at 5 km/h. At 9:12, Michal followed him on a bike at a speed of 20 km/h. At what time did Michal Petra run, and how many kilometers did he cover?
- Two cities
The car goes from city A to city B at an average speed of 70 km/h and 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 will take 8 minutes less. What is the distance between cities A and B? - Two pumps together
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 simultaneously? - Water current speed.
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. - Three pumps We are filling the pool. The pool would fill the first pump in 12 hours and the second in 15 hours. If all three pumps ran simultaneously, they would fill the pool for 4 hours. How long would the pool fill only with the third pump?
The pool contains 220 m³ of water. Workers can empty the pool either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A, and how many from pipe B?Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
