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distance (s)=100m time T₁=10 T₂=10.2 T₃=10.4 T₄=10.6 by v= t s ​ we get V₁= 10 100 ​ V₁=10m/s
V₂= 10.2 100 ​ V₂=9.8m/s
V₃= 10.4 100 ​ V₃=9.61 m/s
V₄= 10.6 100 ​ V₄=9.43 m/s
V₁:V₂:V₃:V₄ = 10 : 9.8 : 9.61 : 9.43

Answered by hardikgupta | 2024-06-10

The ratio of their speeds is 15 : 14.85 : 14.70 : 14.55.
To find the ratio of their speeds, we first need to understand that speed is the distance traveled divided by the time taken to travel that distance. Since all runners are running the same distance (100 meters), their speeds will be inversely proportional to the time they take to complete the race. This means that the faster the runner, the higher the speed.
Let's denote the speeds of the runners who took 10 sec., 10.2 sec., 10.4 sec., and 10.6 sec. to complete the race as v 1 ​ , v 2 ​ , v 3 ​ , and v 4 ​ respectively. The distance d \[/tex]) is constant for all runners, which is 100 meters. The speed of each runner is calculated as: v i ​ = t i ​ d ​
where t_i \) is the time taken by the [tex]\( i \)- runner.
For the four runners, we have:
v 1 ​ = 10 100 ​ = 10 m/s
v 2 ​ = 10.2 100 ​ ≈ 9.80 m/s
v 3 ​ = 10.4 100 ​ ≈ 9.62 m/s
v 4 ​ = 10.6 100 ​ ≈ 9.43 m/s
Now, to find the ratio of their speeds, we divide each speed by the speed of the slowest runner (which is \( v_4 \)):
v 4 ​ v 1 ​ ​ = 9.43 10 ​ ≈ 1.060
v 4 ​ v 2 ​ ​ = 9.43 9.80 ​ ≈ 1.039
v 4 ​ v 3 ​ ​ = 9.43 9.62 ​ ≈ 1.020
v 4 ​ v 4 ​ ​ = 1
To express these ratios as a common ratio, we can multiply each by a factor that makes the denominator a whole number. In this case, we can multiply by 14.55 (the smallest speed inverted) to get:
v 4 ​ v 1 ​ ​ × 14.55 ≈ 15
v 4 ​ v 2 ​ ​ × 14.55 ≈ 14.85
v 4 ​ v 3 ​ ​ × 14.55 ≈ 14.70
v 4 ​ v 4 ​ ​ × 14.55 = 14.55
Therefore, the ratio of their speeds is 15 : 14.85 : 14.70 : 14.55 \)

Answered by AnkitM | 2024-06-25

The ratio of the runners' speeds, based on their completion times of 10 sec, 10.2 sec, 10.4 sec, and 10.6 sec for a 100m race, is approximately 15:14.85:14.70:14.55. Each speed was calculated using the formula v = t d ​ , with the common distance of 100 meters. The final ratio reflects their relative speeds based on the time taken.
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Answered by AnkitM | 2024-12-24

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Answered by DrRayan | 2025-07-04