average speed- not the most difficult concept in mathematics and physics. However, the simplicity of this concept is often deceiving. It must be constantly remembered that the average speed is a value equal to the ratio of the path traversed by the body to the time during which this path traversed. Consider a series of tasks from (FIPI) for the OGE.
Objective 1. The first 105 km the car drove at a speed of 35 km / h, the next 120 km - at a speed of 60 km / h, and the last 500 km - at a speed of 100 km / h. Find the average speed of the car along the way.
Solution. To find the average speed of movement, it is necessary to divide the entire distance traveled by the total time spent. The problem says about three sections of the path, the length of each is known. Let's find the time of movement at each site.
105: 35 = 3 (hours)
120: 60 = 2 (hours)
500: 100 = 5 (hours)
All the time spent is 3 + 2 + 5 = 10 hours.
The length of the covered path is 105 + 120 + 500 = 725 km.
The average speed is 725: 10 = 72.5 km / h.
Answer: 72,5
Objective 2.The car drove the first half of the way at a speed of 69 km / h, and the second - at a speed of 111 km / h. Find the average speed of the car along the way.
Solution.Let us denote the entire traversed path through 2 S ... Then the time spent on the first half of the journey is S / 69, and the second S / 111, all elapsed time is
S / 69 + S / 111 = 180 S / (69 * 111).
Then the average speed is 2 S: 180 S / (69 * 111) = 2 * 69 * 111/180 = 85.1 km / h
Answer: 85,1
Objective 3.The first 2 hours the car drove at a speed of 45 km / h, the next 2 hours at a speed of 35 km / h, and the last 4 hours at a speed of 105 km / h. Find the average speed of the car along the way.
Solution. To find the average speed of movement, it is necessary to divide the entire distance traveled by the total time spent.
All the time spent is equal to 2 + 2 + 4 = 8 hours.
The length of the covered path is 45 * 2 + 35 * 2 + 105 * 4 = 580 km.
The average speed is 580: 8 = 72.5 km / h.
Answer: 72,5
Tasks for an independent solution.
1. The car drove the first half of the route at a speed of 42 km / h, and the second - at a speed of 102 km / h. Find the average speed of the car along the way.
2. The car drove the first half of the route at a speed of 52 km / h, and the second - at a speed of 78 km / h. Find the average speed of the car along the way.
3. The car drove the first half of the route at a speed of 60 km / h, and the second - at a speed of 84 km / h. Find the average speed of the car along the way.
4. The car drove the first half of the route at a speed of 36 km / h, and the second - at a speed of 108 km / h. Find the average speed of the car along the way.
5. The car drove the first half of the route at a speed of 36 km / h, and the second at a speed of 72 km / h. Find the average speed of the car along the way.
6. The car drove the first half of the route at 78 km / h, and the second at 91 km / h. Find the average speed of the car along the way.
7. The car drove the first half of the route at 39 km / h, and the second at 51 km / h. Find the average speed of the car along the way.
8. The car drove the first half of the route at a speed of 30 km / h, and the second - at a speed of 45 km / h. Find the average speed of the car along the way.
9. The car drove the first half of the route at a speed of 45 km / h, and the second at a speed of 90 km / h. Find the average speed of the car along the way.
10. The car drove the first half of the route at a speed of 40 km / h, and the second - at a speed of 85 km / h. Find the average speed of the car along the way.
11. The car drove the first half of the way at a speed of 55 km / h, and the second - at a speed of 70 km / h. Find the average speed of the car along the way.
12. The car drove the first half of the way at a speed of 42 km / h, and the second - at a speed of 48 km / h. Find the average speed of the car along the way.
13. The car drove the first half of the way at a speed of 84 km / h, and the second - at a speed of 96 km / h. Find the average speed of the car along the way.
14. The car drove the first half of the way at a speed of 90 km / h, and the second - at a speed of 110 km / h. Find the average speed of the car along the way.
15. The car drove the first half of the way at a speed of 36 km / h, and the second - at a speed of 99 km / h. Find the average speed of the car along the way.
16. The car drove the first half of the way at a speed of 84 km / h, and the second - at a speed of 108 km / h. Find the average speed of the car along the way.
17. The car drove the first half of the way at a speed of 54 km / h, and the second - at a speed of 90 km / h. Find the average speed of the car along the way.
18. The car drove the first half of the way at a speed of 34 km / h, and the second - at a speed of 51 km / h. Find the average speed of the car along the way.
19. The car drove the first half of the way at a speed of 60 km / h, and the second - at a speed of 90 km / h. Find the average speed of the car along the way.
20. The first 5 hours the car drove at a speed of 60 km / h, the next 3 hours at a speed of 100 km / h, and the last 4 hours at a speed of 75 km / h. Find the average speed of the car along the way.
21. The first 2 hours the car drove at a speed of 80 km / h, the next 2 hours - at a speed of 50 km / h, and the last 4 hours - at a speed of 90 km / h. Find the average speed of the car along the way.
22. The first 4 hours the car drove at a speed of 50 km / h, the next 2 hours at a speed of 90 km / h, and the last 4 hours at a speed of 45 km / h. Find the average speed of the car along the way.
23. The first 5 hours the car drove at a speed of 70 km / h, the next 3 hours - at a speed of 35 km / h, and the last 2 hours - at a speed of 80 km / h. Find the average speed of the car along the way.
24. The first 5 hours the car drove at a speed of 100 km / h, the next 2 hours at a speed of 50 km / h, and the last 3 hours at a speed of 55 km / h. Find the average speed of the car along the way.
25. The first 2 hours the car drove at a speed of 45 km / h, the next 4 hours - at a speed of 100 km / h, and the last 2 hours - at a speed of 75 km / h. Find the average speed of the car along the way.
26. The first 3 hours the car drove at a speed of 115 km / h, the next 2 hours at a speed of 65 km / h, and the last 4 hours at a speed of 95 km / h. Find the average speed of the car along the way.
27. The first 5 hours the car drove at a speed of 110 km / h, the next 3 hours - at a speed of 50 km / h, and for the last 3 hours - at a speed of 60 km / h. Find the average speed of the car along the way.
28. The first 5 hours the car drove at a speed of 100 km / h, the next 3 hours at a speed of 75 km / h, and the last 2 hours at a speed of 50 km / h. Find the average speed of the car along the way.
29. The first 3 hours the car drove at a speed of 100 km / h, the next 4 hours at a speed of 95 km / h, and the last 3 hours at a speed of 50 km / h. Find the average speed of the car along the way.
30. The first 2 hours the car drove at a speed of 70 km / h, the next 3 hours - at a speed of 60 km / h, and the last 5 hours - at a speed of 45 km / h. Find the average speed of the car along the way.
31. The first 5 hours the car drove at a speed of 55 km / h, the next 5 hours - at a speed of 75 km / h, and the last 5 hours - at a speed of 80 km / h. Find the average speed of the car along the way.
32. The first 5 hours the car drove at a speed of 85 km / h, the next 5 hours - at a speed of 65 km / h, and for the last 5 hours - at a speed of 60 km / h. Find the average speed of the car along the way.
33. The first 2 hours the car drove at a speed of 65 km / h, the next 4 hours - at a speed of 105 km / h, and the last 4 hours - at a speed of 80 km / h. Find the average speed of the car along the way.
34. The first 3 hours the car drove at a speed of 110 km / h, the next 3 hours - at a speed of 35 km / h, and for the last 3 hours - at a speed of 50 km / h. Find the average speed of the car along the way.
35. The first 5 hours the car drove at a speed of 90 km / h, the next 2 hours - at a speed of 115 km / h, and for the last 3 hours - at a speed of 40 km / h. Find the average speed of the car along the way.
36. The first 4 hours the car drove at a speed of 50 km / h, the next 4 hours at a speed of 80 km / h, and the last 4 hours at a speed of 35 km / h. Find the average speed of the car along the way.
37. The first 2 hours the car drove at a speed of 70 km / h, the next 3 hours - at a speed of 65 km / h, and the last 3 hours - at a speed of 75 km / h. Find the average speed of the car along the way.
38. The first 3 hours the car drove at a speed of 35 km / h, the next 2 hours - at a speed of 60 km / h, and the last 5 hours - at a speed of 100 km / h. Find the average speed of the car along the way.
39. The first 90 km the car drove at a speed of 45 km / h, the next 400 km - at a speed of 100 km / h, and the last 150 km - at a speed of 75 km / h. Find the average speed of the car along the way.
40. The first 345 km the car drove at a speed of 115 km / h, the next 130 km - at a speed of 65 km / h, and the last 380 km - at a speed of 95 km / h. Find the average speed of the car along the way.
41. The first 550 km the car drove at a speed of 110 km / h, the next 150 km - at a speed of 50 km / h, and the last 180 km - at a speed of 60 km / h. Find the average speed of the car along the way.
42. The first 500 km the car drove at a speed of 100 km / h, the next 225 km - at a speed of 75 km / h, and the last 100 km - at a speed of 50 km / h. Find the average speed of the car along the way.
43. The first 300 km the car drove at a speed of 100 km / h, the next 380 km - at a speed of 95 km / h, and the last 150 km - at a speed of 50 km / h. Find the average speed of the car along the way.
44. The first 140 km the car drove at a speed of 70 km / h, the next 180 km - at a speed of 60 km / h, and the last 225 km - at a speed of 45 km / h. Find the average speed of the car along the way.
45. The first 275 km the car drove at a speed of 55 km / h, the next 375 km - at a speed of 75 km / h, and the last 400 km - at a speed of 80 km / h. Find the average speed of the car along the way.
46. The first 425 km the car drove at 85 km / h, the next 325 km - at 65 km / h, and the last 300 km - at 60 km / h. Find the average speed of the car along the way.
47. The first 130 km the car drove at 65 km / h, the next 420 km - at 105 km / h, and the last 320 km - at 80 km / h. Find the average speed of the car along the way.
48. The first 90 km the car drove at a speed of 45 km / h, the next 70 km - at a speed of 35 km / h, and the last 420 km - at a speed of 105 km / h. Find the average speed of the car along the way.
49. The first 300 km the car drove at a speed of 60 km / h, the next 300 km - at a speed of 100 km / h, and the last 300 km - at a speed of 75 km / h. Find the average speed of the car along the way.
50. The first 160 km the car drove at 80 km / h, the next 100 km - at 50 km / h, and the last 360 km - at 90 km / h. Find the average speed of the car along the way.
51. The first 200 km the car drove at a speed of 50 km / h, the next 180 km - at a speed of 90 km / h, and the last 180 km - at a speed of 45 km / h. Find the average speed of the car along the way.
52. The first 350 km the car drove at 70 km / h, the next 105 km - at 35 km / h, and the last 160 km - at 80 km / h. Find the average speed of the car along the way.
53. The first 500 km the car drove at a speed of 100 km / h, the next 100 km - at a speed of 50 km / h, and the last 165 km - at a speed of 55 km / h. Find the average speed of the car along the way.
54. The first 330 km the car drove at a speed of 110 km / h, the next 105 km - at a speed of 35 km / h, and the last 150 km - at a speed of 50 km / h. Find the average speed of the car along the way.
55. The first 450 km the car drove at a speed of 90 km / h, the next 230 km - at a speed of 115 km / h, and the last 120 km - at a speed of 40 km / h. Find the average speed of the car along the way.
56. The first 200 km the car drove at 50 km / h, the next 320 km - at 80 km / h, and the last 140 km - at 35 km / h. Find the average speed of the car along the way.
57. The first 140 km the car drove at a speed of 70 km / h, the next 195 km - at a speed of 65 km / h, and the last 225 km - at a speed of 75 km / h. Find the average speed of the car along the way.
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