Harmonic mean - practice problems - page 2 of 9
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 170
- Sequence 11
What is the nth term of this sequence 1, 1/2, 1/3, 1/4, 1/5 ...? - 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. - Working together
One painter painted the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together? - Probability 4665
We have three series of products. We select one product for quality control. Determine the probability of finding a low-quality product if the first batch contains 2/3, the second batch 7/9, and the third batch 3/4 quality 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? - Average speed
The car drove from city A to city B at 40 km/h and back to city A at a speed of 80 km/h. What was the average speed of the car? - The factory
The factory z can complete an order in 12 days, factory p in 18 days. How many days does an order completed when the first two days work only the factory z and then both factories? - Tributaries
The first tributary fills the pool with water in 15 hours. The second tributary fills the pool in 10 hours. For how many hours is the pool filled with both tributaries? - Apartment 81654
A woman cleans an apartment in 8 hours and a man in 10 hours. How many hours will they clean together? - A person
A person buys 10 kg of commodity A at a rate of 2 kg per dollar, 20 kg of commodity b at a rate of 5 kilograms per dollar, and 30 kg of commodity C at a rate of 10 kg per dollar. Find the average price of kg per dollar. - Three altitudes
A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - 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? - Excavators 82208
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? - Together 3781
Milos would do the work himself in 5 hours. How much would it take Dan to do the job together in two hours? - Performance 20233
How many% need to increase performance, if the work we have planned for five days we have to manage in 3 days. - Together 5931
The tank will be filled with the first inlet in 5 hours and the second in 12 hours. How long would it take to fill the tank together? - Two pumps
Pump A takes twice as long to fill a tank as B. Together, they take 2 hours to fill the tank. How long does each one take to fill the tank by itself? - Bricklayers
When a bricklayer works to redeem the house in 8 days, the other bricklayer will be finished in 10 days. How long will it take to make three such houses together? - Turners
Two turners perform joint work in 3 hours. The first-turner would perform the job himself in 7 hours. How long would the same job last for a second-turner if he worked alone? - Pumping
The tank is filled with a larger pump in 12 hours and with a second pump in 15 hours. For how long does the tank fill when both pumps are switched on at the same time?
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