To solve this problem, we need to calculate the perimeter of the race track and then determine how many laps are needed to complete 12 km.

Step 1: Calculate the perimeter of the track

The track is rectangular with semicircular ends. The straight sides are each 125 m, and the semicircular parts have a diameter of 50 m (radius = 25 m).

• The length of the two straight sides is: $125 \, \text{m} + 125 \, \text{m} = 250 \, \text{m}$

• The length of the two semicircular ends (which form a full circle) is: $\text{Circumference of a circle} = 2 \pi r = 2 \pi (25) = 50\pi \, \text{m}$ Approximating $\pi \approx 3.14$, the circular part's length is: $50 \times 3.14 = 157 \, \text{m}$

• Total perimeter of the track: $250 \, \text{m} + 157 \, \text{m} = 407 \, \text{m}$

Step 2: Calculate the number of laps

• Total distance Inaya needs to run: $12 \, \text{km} = 12,000 \, \text{m}$

• Number of complete laps: $\text{Number of laps} = \frac{\text{Total distance}}{\text{Perimeter of track}} = \frac{12,000}{407} \approx 29.48$

Since she can only complete whole laps, Inaya will need to run 30 complete laps.

Do you want me to break down or explain any part further?

Related Questions:

1. How is the formula for the circumference of a circle derived?
2. If Inaya wants to run 15 km instead of 12 km, how many laps would that be?
3. How would the solution change if the width of the track was 60 m instead of 50 m?
4. What is the time it will take for Inaya to complete 30 laps if she runs at a speed of 6 m/s?
5. How can the perimeter be calculated more accurately without approximating $\pi$?

Tip:

When working with circular or semicircular shapes, always identify the radius first, as it is key to calculating circumference and other properties.