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 and set up equations for the two parts of the journey. Let D be the total distance of the journey in km. For the first part of the journey: The distance covered is D_1 = (1)/(3)D. The speed is S_1 = 30 km/h. The time taken for the first part is T_1 = (D_1)/(S_1) = (1)/(3)D30 = (D)/(90) hours. For the second part of the journey (remaining distance): The remaining distance is D_2 = D - D_1 = D - (1)/(3)D = (2)/(3)D. The speed is S_2 = 40 km/h. The time taken for the second part is T_2 = (D_2)/(S_2) = (2)/(3)D40 = (2D)/(120) = (D)/(60) hours. Step 2: Use the total time to form an equation. The total time for the whole journey is given as 4 hours. So, T_1 + T_2 = 4. (D)/(90) + (D)/(60) = 4 Step 3: Solve the equation for D. To solve for D, find the least common multiple (LCM) of the denominators 90 and 60. The LCM(90, 60) = 180. Multiply the entire equation by 180 to eliminate the denominators: 180 ( (D)/(90) ) + 180 ( (D)/(60) ) = 4 × 180 2D + 3D = 720 5D = 720 D = (720)/(5) D = 144 km Step 4: Express the answer as a repeating decimal. Since 144 is an integer, it can be written as a repeating decimal by adding a decimal point and an infinite sequence of zeros. D = 144.0 km The total distance of the journey is 144.0 km. That's 2 down. 3 left today — send the next one.