# Pilsen circus

The arrival of the circus in Pilsen was seen in the morning at 08:00 by a citizen of the city. He passed this information on 08:15 to three other residents of the city. Each of these three people then informed the other three residents at 08:30, and again at 08:45, they reported the arrival of the circus every three to other uninformed residents. This chain continued the same way every other quarter of an hour. What time did all residents of Pilsen first know about the arrival of the circus when each person was only informed once? Plzen = 171,707 inhabitants.

Result

t = 11:00

#### Solution:

$s=171707 \ \\ \ \\ q=3 \ \\ a_{1}=1 \ \\ \ \\ \ \\ s=a_{1} \cdot \ \dfrac{ q^n-1 }{ q-1 } \ \\ \ \\ s/a_{1} \cdot \ (q-1)+1=q^n \ \\ \ \\ \ln s/a_{1} \cdot \ (q-1)+1=n \ln q \ \\ \ \\ n=\dfrac{ \ln (s/a_{1} \cdot \ (q-1)+1) }{ \ln(q) }=\dfrac{ \ln (171707/1 \cdot \ (3-1)+1) }{ \ln(3) } \doteq 11.6025 \ \\ \ \\ t_{1}=8.00 + 0.25 \cdot \ (n-1)=8.00 + 0.25 \cdot \ (11.6025-1) \doteq 10.6506 \ \\ \ \\ t=\lceil t_{1} \rceil=\lceil 10.6506 \rceil=11=11:00$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert time units like minutes to seconds?

## Next similar math problems:

1. Troops
There are two leaders in the tourist group, with an average age of 30 years and several children with an average age of 10 years. The total age of the group is 12 years. How many children are in the group?
2. Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
3. Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
4. Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
5. Ducats
The king divided the ducats to his three sons in a ratio of 2: 5: 4. How many ducats the king divided them if the youngest received 260 ducats, which was the least of all sons.
6. Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
7. Large family
I have as many brothers as sisters and each my brother has twice as many sisters as brothers. How many children do parents have?
8. Runners
If John has a running speed of 3.5miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 am and Lucy starts running at 10:30 am, at what time will they meet? (as soon as possible)
9. Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
10. Growth of wood
The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
11. Aircraft angines
The two engines of the aircraft are enough to supply the fuel for five hours of operation. However, one of the engines has a malfunction and thus consumes one-third more fuel. How long can the plane be in the air before it runs out of fuel? After an hour
12. Three faces of a cuboid
The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
13. Mortage hypo loan
The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?
14. Water container
The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
15. Alcohol mixing
How much 64% of the alcohol must be poured into 6 liters of 85% alcohol to produce 79% alcohol?
16. Hiking trail
The newly built hiking trail leads 25% through the field, 3/8 of the trail leads through the forest and the remaining 9 km along the river. How long is the train?
17. Nádoba
Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby?