# Algebra - problems - page 11

1. Camp
In a class are 26 children. During the holidays 16 children were in the camps and 14 children on holiday with their parents. Determine the minimum and maximum number of children that may have been in the camp and on holiday with their parents at the same
2. Water inlets
Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after?
3. Train
A passenger train traveled for 2 hours 74 km. 3.1 hours after its departure started fast train and caught it on 186 km. How many km/h is different its average speeds?
4. Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
5. Father and son
Father and son are together 80 years. Son is 28 years younger than father. How old is the son?
6. Division
Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 6:1:4. How many candies should each get if in bag were 88?
7. Apples
Hanka has 6 apples more than Juro and 7 apples less than Mirka. Mirka has 23 apples. How many apples has Hanka and how many Juro?
8. Cyclists
Cyclist who rides at an average speed 16 km/h travels trip distance 10 min before the cyclist who rides at an average speed 11 km/h. What is the length of this cyclist trip(distance in km)?
9. Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
10. Hollow sphere
Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
11. Scouts
The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
12. Tanker
An oil tanker can be emptied by the first pump in 4.9 hours. Second pump can empty an tanker in 8 hours. If the first pump started at 4:00 and second 1.4 hour later, at what time will the tanker be empty?
13. Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
14. Primes 2
Which prime numbers is number 2025 divisible?
15. Triangle angles
The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
16. Amazing number
An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.
17. Truck
Truck went for 4 hours and 30 minutes. If truck increase speed by 11 km/h, went same distance in 2 hours. Calculate this distance.
18. Geodesist
Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
19. Mailbox
Mailbox is opening at regular intervals 3 times a day. The first time is opened at 8:00 and the last at 19:00. Calculate hours when mailbox is opened during day.
20. Spherical segment
Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.

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