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: Define variables for distance and speed. Let the total distance be D. The car covers the first part of the distance (d_1) with speed v_1. d_1 = (1)/(3)D v_1 = 20 km/h The car covers the remaining distance (d_2) with speed v_2. d_2 = D - (1)/(3)D = (2)/(3)D v_2 = 60 km/h Step 2: Calculate the time taken for each part of the journey. The formula for time is t = distancespeed. Time for the first part (t_1): t_1 = (d_1)/(v_1) = (1)/(3)D20 km/h = (D)/(3 × 20) h = (D)/(60) h Time for the second part (t_2): t_2 = (d_2)/(v_2) = (2)/(3)D60 km/h = (2D)/(3 × 60) h = (2D)/(180) h = (D)/(90) h Step 3: Calculate the total time taken. Total time T = t_1 + t_2. T = (D)/(60) + (D)/(90) To add these fractions, find a common denominator, which is 180. T = (3D)/(180) + (2D)/(180) = (3D + 2D)/(180) = (5D)/(180) = (D)/(36) h Step 4: Calculate the average speed. The formula for average speed is Average speed = Total distanceTotal time. Average speed = (D)/(T) = (D)/(D)36 Average speed = D × (36)/(D) = 36 km/h The average speed is 36 km/h. This corresponds to option (D). The final answer is 36 km/h.