To solve the problem in the image, let's analyze the track and its components step by step:

Geometry of the Track

• The track consists of two straight parallel line segments and two semicircles at the ends.
• Inner dimensions:
  • Length of each straight segment = 110 m
  • Radius of each semicircle = $\frac{90 \, \text{m}}{2} = 45 \, \text{m}$
• Outer dimensions:
  • The width of the track is 10 m.
  • Radius of the outer semicircle = $45 + 10 = 55 \, \text{m}$

Part (a): Distance Biked by Ismail (Inner Edge)

1. Length of the two straight segments: $2 \times 110 = 220 \, \text{m}$
2. Perimeter of the two semicircles (inner edge): $\text{Perimeter of circle} = 2\pi r \implies \text{Half circle} = \pi r$ So, for two semicircles: $2 \times (\pi \times 45) = 90\pi \, \text{m}$. Approximate $\pi \approx 3.1416$: $90\pi \approx 282.74 \, \text{m}$
3. Total distance for one lap (inner edge): $\text{Distance} = 220 + 282.74 = 502.74 \, \text{m}$ Rounded to the nearest tenth: 502.7 m

Part (b): Distance Biked by Carey (Outer Edge)

1. Length of the two straight segments: $2 \times 110 = 220 \, \text{m}$ (same as inner edge).
2. Perimeter of the two semicircles (outer edge): $2 \times (\pi \times 55) = 110\pi \, \text{m}$ Approximate $\pi$: $110\pi \approx 345.58 \, \text{m}$
3. Total distance for one lap (outer edge): $\text{Distance} = 220 + 345.58 = 565.58 \, \text{m}$ Rounded to the nearest tenth: 565.6 m

Part (c): Difference in Distances

The difference between Carey’s and Ismail’s distances: $565.6 - 502.7 = 62.9 \, \text{m}$ So, the difference is 62.9 m.

Final Answers

(a) Ismail bikes 502.7 m in one lap.
(b) Carey bikes 565.6 m in one lap.
(c) The difference is 62.9 m.

Would you like a breakdown of specific calculations or further clarifications?

Here are five related questions:

1. How would the total lap distance change if the width of the track were increased?
2. How does the semicircle radius affect the total lap length?
3. What if the track were an ellipse instead of a semicircle? How would you calculate the perimeter?
4. Can you calculate the area of the track's surface?
5. What is the percentage increase in distance for Carey compared to Ismail?

Tip: Always verify semicircular and straight sections separately when analyzing track geometries!