Expression of a variable from the formula + harmonic mean - practice problems
Number of problems found: 34
- 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. - 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? - Together 81046
Two painters are painting the factory fence together. If everyone worked alone, the first would finish the job in 16 days, the second in 20 days. When will they finish the work together? - Developed 64664
In the first stage, the cyclist covered 70 km at a speed of 22.1 km/h. In the second stage, he covered 40 km (a total of 110 km), and his average speed increased to 22.9 km/h. What an average speed he developed in the second stage!
- Harmonic mean
If x, y, and z form a harmonic progression, y is the harmonic mean of x and z. Find the harmonic mean of the numbers 6 and 5. - Harmonic series
Insert four members between 5/3 and 5/11 to form a harmonic series (means). - Insert 7
Insert five harmonic means between 3 and 18 - HP - harmonic progression 2 Compute the 16th term of the HP if the 6th and 11th terms of the harmonic progression are 10 and 18, respectively.
- Between two bus stops
Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that he would have arrived at the bus stop if he had run to one or the other. The average bus speed is 60 km/h. What is Wanda's average running spee
- Average speed
The truck drove 1/2 of the way on the highway at 80 km/h. The other half of the way, 20 km/h. Calculate the average speed. - Two parts journey The car driver plans to drive to a distance of 30 km in 0.5 hours. For twenty minutes, he follows the column at a speed of 30 km/h. What speed would he have to go in the remaining time?
- 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. - 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, - 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?
- 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? - A report
Maricris can type a committee report in 5 hours. Jane helped Maricris, and together they finished the report in 3 hours. How long would it take Jane to complete the report she had worked on alone? - Minutes 7177
The tank holds 140 liters of water. It is filled with a tap in 5 minutes, and the drain is emptied in 7 minutes. How long will it take for the empty tank to fill if we open the faucet and drain it? - Soldier
An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench every 40 hours. How many hours will the ditch dig all three together? - Summer tires
Three tire servants must change the summer tires on six cars in 2 hours. Mark's replacement would take 4.5 hours, Jirka would do it in 3 hours and 10 minutes, and Honza in 4 hours. Will they be able to replace all tires at the desired time?
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