Time + harmonic mean - math problems
- Panel house
The construction company has two groups of workers. Group A has more members than B. Panel house was insulated by group A in 10 days. The same block of flats was insulated together in 6 days. How many days would group B block insulate?
- Between two bus stops
Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h. What is the average
- 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 done work in 12 days?
- Athletic competition
In a 400 meter athletic competition, a participant covers the distance as 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
- 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?
Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together?
- Two cyclists 2
At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,
- Two cities
The car goes from city A to city B at an average speed of 70 km/h, 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 would 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 at the same time?
- 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 first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump?
- Working together
One worker performs work in 3 days, the second in 5 days. How much do they work together?
- Express train
International express train drove from Kosice to Teplice. In the first 279 km, the track was repaired, and therefore it was moving at a speed of 10km/h less than it was scheduled to drive. The rest of the 465 km trip has increased the speed by 8 km/h than
- The factory
The factory z can complete an order in 12 days, factory p in 18 days. For how many days does an order completed when the first two days work only the factory z and then both factories?
- Water reservoir
One drain hole emptied the water from the tank for 20 hours, with the second drain for 30 hours. How long will the water drain from this tank if we open two drains simultaneously?
The first harvester will harvest the grain from the field in 20 hours, the second, the more powerful in 10 hours. How long will take harvest this field by both harvesters, if the second harvester has to be set up first and this takes 2 hours? The first ha
- 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 alone?
An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together?
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