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1 month ago

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In a 5000 m race, the athletes run 12 1/2 laps; each lap is 400 m.Kara runs the race at a constant pace and finishes in 17.9 min

.Hannah runs the race in a blistering 15.3 min, so fast that she actually passes Kara during the race. How many laps has Hannah run when she passes Kara?

1 answer:

Softa [3K]1 month ago

3 0

Answer:

Approximately, Hannah has completed 7 laps.

Solution:

Based on the provided details:

The complete distance to run, D = 5000 m

The distance for one lap, x = 400 m

Kara's time taken, $t_{K} = 17.9 min = 17.9\times 60 = 1074 s$

Hannah's time taken, $t_{H} = 15.3 min = 15.3\times 60 = 918 s$

The speed for both Kara and Hannah can be determined as follows:

$v_{K} = \frac{D}{t_{K}} = \frac{5000}{1074} = 4.65 m/s$

$v_{H} = \frac{D}{t_{H}} = \frac{5000}{918} = 5.45 m/s$

The time taken for each lap is represented by:

$(v_{H} - v_{K})t = x$

$(5.45 - 4.65)\times t = 400$

$t = \frac{400}{0.8}$

t = 500 s

Thus, the distance that Hannah covers in 't' seconds is given by:

$d_{H} = v_{H}\times t$

$d_{H} = 5.45\times 500 = 2725 m$

The number of laps completed by Hannah when she overtakes Kara:

$n_{H} = \frac{d_{H}}{x}$

$n_{H} = \frac{2725}{400} = 6.8$ ≈ 7 laps

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