New math problems
- The cruise ship
The cruise ship has a speed of 12 km / h at a calm surface. When we sail 45 km along the river and 45 km back, it took us exactly 8 hours. Which (constant) speed of flow of the river?
- Sphere equation
Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
The first worker would need less than 4 hours to complete the task than the other worker. In fact, both workers worked for two hours together, then the first worker did the remaining work himself. In what proportion should the remuneration of the workers b
- Number with ones
The first digit of the number is 1, if we move this digit to the end we get a 3 times higher number, which is the number?
One-eighth of the trees in the fruit plant in winter froze and one-twelfth of damaged disease and pests. Healthy trees remained 152. Is it enough to supply 35 trees to restore the original number of trees in the orchard?
The rectangular face of a drawer has a perimeter of 108 cm and a width of 18cm. Find the length and the area of the rectangular face of the drawer.
- Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
- Water block
A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
- Grandfather and grandmother
The old mother is 5 years younger than the old father. Together they are 153 years old. How many years has each of them?
- Two trains
There were 159 freight wagons on the railway station creating 2 trains. One had 15 more wagons than the other. How many wagons did each train have?
Mother bought 21 desserts on the occasion of Mirka's birthday one tips was 9 CZK and the kremlin cost 12 CZK. For all desserts, she paid 213 CZK. How many kremlins and how many tips mums did buy?
- Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They
- Pupil age
I am a pupil of the primary school, I spent 1/4 of my age on the exercise of parents with children, 1/3 on drawing, 1/6 on flute. I did not have a ring for the first three years of my life and never went to two rings at once. How old am I?
- Equation of circle 2
Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
- Repay, interest, loan
Ramchacha takes a loan amount of 240000 from a bank for constructing a house at the rate of simple interest of 12% per annum. After 1 yr. of taking the loan he rents the house at the rate of 5200 per month. Determine the number of years he would take to re
- Train and walker
Walker passes an hour 5 km. Express train per hour 100 km. Walker went 4 hours. How many minutes took the distance express train?
Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
- Volume and body diagonal
Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.