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Kibet ran around a track five times. The track is a rectangle with two semicircles at its ends. The length of the straight sections is 110 m and the diameter of each semicircle is 70 m. Calculate the

Mathematics

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Answer

2.2 km\text{2.2 km}

Step-by-step solution

4 steps

here's the solution to the problem:

The diagram shows a track composed of a rectangle with two semicircles at its ends. Kibet ran around this track five times. We need to find the total distance covered in kilometers.

  1. Determine the dimensions of the track.

    The length of the straight sections is 110 m110 \text{ m}.
    The diameter of each semicircle (which is also the width of the rectangular part) is 70 m70 \text{ m}.

  2. Calculate the perimeter of one lap of the track.

    The perimeter of the track consists of two straight sections and the circumference of two semicircles (which combine to form one full circle).
    Length of two straight sections = 2×110 m=220 m2 \times 110 \text{ m} = 220 \text{ m}.
    Circumference of one full circle (from the two semicircles) = π×diameter\pi \times \text{diameter}.
    Using the approximation π=227\pi = \frac{22}{7}:
    Circumference = 227×70 m=22×10 m=220 m\frac{22}{7} \times 70 \text{ m} = 22 \times 10 \text{ m} = 220 \text{ m}.
    Perimeter of one lap = (Length of straight sections) + (Circumference of full circle)
    Perimeter of one lap = 220 m+220 m=440 m220 \text{ m} + 220 \text{ m} = 440 \text{ m}.

  3. Calculate the total distance Kibet covered for five laps.

    Total distance = Perimeter of one lap ×\times Number of laps
    Total distance = 440 m×5=2200 m440 \text{ m} \times 5 = 2200 \text{ m}.

  4. Convert the total distance from meters to kilometers.

    Since 1 km=1000 m1 \text{ km} = 1000 \text{ m}:
    Total distance in kilometers = 2200 m1000 m/km=2.2 km\frac{2200 \text{ m}}{1000 \text{ m/km}} = 2.2 \text{ km}.

    Kibet covered a total distance of 2.2 km\text{2.2 km}.

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