Answer:
No. of laps of Hannah are 7 (approx).
Solution:
According to the question:
The total distance to be covered, D = 5000 m
The distance for each lap, x = 400 m
Time taken by Kara, [tex]t_{K} = 17.9 min = 17.9\times 60 = 1074 s[/tex]
Time taken by Hannah, [tex]t_{H} = 15.3 min = 15.3\times 60 = 918 s[/tex]
Now, the speed of Kara and Hannah can be calculated respectively as:
[tex]v_{K} = \frac{D}{t_{K}} = \frac{5000}{1074} = 4.65 m/s[/tex]
[tex]v_{H} = \frac{D}{t_{H}} = \frac{5000}{918} = 5.45 m/s[/tex]
Time taken in each lap is given by:
[tex](v_{H} - v_{K})t = x[/tex]
[tex](5.45 - 4.65)\times t = 400[/tex]
[tex]t = \frac{400}{0.8}[/tex]
t = 500 s
So, Distance covered by Hannah in 't' sec is given by:
[tex]d_{H} = v_{H}\times t[/tex]
[tex]d_{H} = 5.45\times 500 = 2725 m[/tex]
No. of laps taken by Hannah when she passes Kara:
[tex]n_{H} = \frac{d_{H}}{x}[/tex]
[tex]n_{H} = \frac{2725}{400} = 6.8[/tex] ≈ 7 laps
The number of laps that Hannah has run when she passes Kara is 7 laps.
The speed of each athlete is calculated as follows;
Kara = (5000) / (17.9 x 60) = 4.66 m/s
Hannah = (5000) / (15.3 x 60) = 5.47 m/s
The time taken in each lap if Hannah passes kara is calculated as follow;
(5.47 - 4.66)t = 400
0.81t = 400
t = 493.83 s
Distance covered by Hannah when she passes kara;
d = 493.83 x 5.47 = 2,701.25 m
n = 2,701.25/400
n = 6.8 ≈ 7 laps.
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