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 minimum green time for pedestrians (G_min). For Road A: G_minA = 21 m1.2 m/s + 7 s = 17.5 s + 7 s = 24.5 s For Road B: G_minB = 14 m1.2 m/s + 7 s = 11.67 s + 7 s = 18.67 s Step 2: Calculate critical flow ratios (y_i) and total critical flow ratio (Y). y_A = 400 V/hr1800 V/hr/lane = 0.2222 y_B = 200 V/hr1800 V/hr/lane = 0.1111 Y = y_A + y_B = 0.2222 + 0.1111 = 0.3333 Step 3: Calculate optimal cycle length using Webster's formula (C_0). Assuming total lost time L = 2 × 4 s = 8 s. C_0 = (1.5L + 5)/(1 - Y) = 1.5(8 s) + 51 - 0.3333 = 12 s + 5 s0.6667 = 17 s0.6667 ≈ 25.5 s Step 4: Determine the minimum cycle length required to satisfy pedestrian green time (C_min). For Road A: C - L (Y)/(y_A) G_minA = (0.3333)/(0.2222) × 24.5 s = 1.5 × 24.5 s = 36.75 s For Road B: C - L (Y)/(y_B) G_minB = (0.3333)/(0.1111) × 18.67 s = 3 × 18.67 s = 56.01 s The maximum required value for (C-L) is 56.01 s. C_min = L + 56.01 s = 8 s + 56.01 s = 64.01 s Step 5: Select the design cycle length. Compare C_0 = 25.5 s and C_min = 64.01 s. The design cycle length is the greater of the two. Design Cycle Length = 64.01 s Got more? Send 'em 📸