A skating champion moves along the circumference of a circle of radius 28 m in 44 sec. How many seconds will it take her to move along the perimeter of a hexagon of side 48 m?

### Concept & Speed, Distance, and Time This problem requires equating the speed of the skater on two different geometric paths. First, calculate the speed using the circular path, then use that speed to find the time taken for the hexagonal path. $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$ ### Step-by-Step Solution * **Step 1: Find the speed on the circular track.** * Radius of the circle, $r = 28$ m. * Perimeter (circumference) of the circle = $2\pi r = 2 \times \frac{22}{7} \times 28$. * Circumference = $2 \times 22 \times 4 = 176$ m. * Time taken for the circle = 44 seconds. * Speed = $\frac{176 \text{ m}}{44 \text{ s}} = 4$ m/s. * **Step 2: Find the time for the hexagonal track.** * Side of the regular hexagon, $a = 48$ m. * Perimeter of the hexagon = $6 \times a = 6 \times 48 = 288$ m. * Time taken = $\frac{\text{Distance}}{\text{Speed}} = \frac{288}{4}$. * Time = $72$ seconds. ### Exam Strategy & Shortcut Instead of calculating the intermediate speed fully, you can set up a ratio since speed is constant: $\frac{\text{Time}_1}{\text{Distance}_1} = \frac{\text{Time}_2}{\text{Distance}_2}$ $\frac{44}{2 \times \frac{22}{7} \times 28} = \frac{T}{6 \times 48} \Rightarrow \frac{44}{176} = \frac{T}{288} \Rightarrow \frac{1}{4} = \frac{T}{288} \Rightarrow T = 72$. ### Common Pitfall A frequent mistake is using the formula for the area instead of the perimeter for the tracks. Always associate "moving along the circumference/perimeter" with boundary length, not internal area. ### Final Answer Therefore, the correct answer is **72**.