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29 May, 05:16

A 30-meter by 70-meter rectangular garden is surrounded by a walkway with a width of 5 meters. Karen is running one lap around the outer edge of the walkway at a rate of 4 km per hour, while her brother is running 2 laps around the inner edge of the walkway twice faster. If they start running at the same time, how many minutes earlier will Karen's brother finish his run?

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  1. 29 May, 05:24
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    Step-by-step explanation:

    The formula for determining the perimeter of a rectangle is expressed as

    Perimeter = 2 (L + W)

    The garden measures 30m * 70m. The perimeter would be

    Perimeter = 2 (30 + 70) = 200m

    If Karen's brother is running 2 laps around the inner edge of the walkway, then the total distance covered is 200 * 2 = 400m

    Converting to km, it becomes

    400/1000 = 0.4km

    If he runs 2 times faster than Karen, then his speed is 2 * 4 = 8km/h

    Time = distance/speed

    Time spent in running the 2 laps is

    0.4/8 = 0.05 hours

    Converting to minutes, it becomes

    0.05 * 60 = 3 minutes

    Since the walkway is 5m, if Karen is running one lap around the outer edge of the walkway, the total length would be (70 + 5 + 5) = 80m

    The width would be (30 + 5 + 5) = 40m. The perimeter is

    2 (80 + 40) = 240 m

    Converting to kilometers, it becomes

    240/100 = 0.24 km

    Time taken by Karen to run 0.24km is

    0.24/4 = 0.06 hours

    Converting to minutes, it becomes

    0.06 * 60 = 3.6 minutes

    The difference in time is

    3.6 - 3 = 0.6 minutes

    Karen's brother finish his run in

    0.6 minutes earlier than Karen.
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