This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the total length of the straight sections. There are two straight sections, each 120 m long. Length of straight sections = 2 × 120 m = 240 m Step 2: Calculate the total length of the curved sections. The track has two semicircular sections. When combined, these two semicircles form one full circle. The diameter of this circle is given as 23 m. The circumference of a circle is given by the formula C = d, where d is the diameter. Length of curved sections = × 23 m = 23 m Step 3: Calculate the total distance of one lap around the track. The total distance is the sum of the lengths of the straight sections and the curved sections. Total distance = 240 m + 23 m Total distance ≈ 240 + 23 × 3.14159265... m Total distance ≈ 240 + 72.25663 m Total distance ≈ 312.25663 m Step 4: Calculate the time taken to run one lap. Emmanuel runs at a constant speed of 4 m/s. The formula for time is Time = DistanceSpeed. Time = 312.25663 m4 m/s Time ≈ 78.0641575 s Step 5: Round the answer to 1 decimal place. Time ≈ 78.1 s The time it takes Emmanuel to run exactly once around the track is 78.1 s.