Units - examples - page 94

1. 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?
2. Square prism Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
3. Lumberjacks Fifteen lumberjacks would take 12 days to destroy the broken trees. How many days would this work require if 5 workers added to it after 4 days?
4. Two cities The distance between cities A and B is 132 km. At 9.00 am, the cyclist started the bike at an average speed of 24 km/h, and at 10.00 h started from the B cyclist at an average speed of 30 km/h. How long and far from A will they both meet?
5. 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%?
6. Base of house Calculate the volume of the bases of a square house, if the base depth is 1.2 m, the width is 40 cm and their outer circumference is 40.7 m.
7. 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?
8. Two trains Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did it tak Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
10. Electric energy There are 875 identical light bulbs in the sports hall lighting for 2 hours. How long does the same amount of electricity consume 100 such bulbs?
11. The tank The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?
12. Saving 9 An amount if \$ 2000 is invested at an interest of 5% per month. if \$ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount have accumula
13. Three pumps The water tank is emptied with the first pump in 6 hours, with the second pump in 2 hours. In order to be emptied in 1 hour, all three pumps had to be started at once. How long will take tank be emptied by only the third pump?
14. Cube into sphere The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
15. Father and sons After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now?
16. Painters Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
17. Minimum surface Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
18. Fruit juice Fruit juice contains 37.5% sugar. How many percents of sugar will be in the flavored mineral that we prepare from 100 grams of fruit juice and 1.4 liters of mineral? (1 liter = 1 kg)
19. Balance of account Theo had a balance of -\$4 in his savings account. After making a deposit, he has \$25 in his account. What is the overall change to his account?
20. Garden The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?

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