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 distance and time for each part of the journey. Part 1: Cycling from home to Mula Trading Centre The distance is given as 30 km. The time taken is given as 2(1)/(2) hours. d_1 = 30 km t_1 = 2.5 hours Part 2: Driving from Mula to a town and back to Mula The distance to the town is 180 km, and he drove back to Mula, so the return distance is also 180 km. The total distance for this part is: d_2 = 180 km + 180 km = 360 km The average speed for this part is 80 km/h. The time taken for this part is: t_2 = DistanceSpeed = 360 km80 km/h = 4.5 hours Part 3: Cycling from Mula back home Mula Trading Centre is 30 km from his home, so the distance back home is 30 km. d_3 = 30 km The average speed for this part is 15 km/h. The time taken for this part is: t_3 = DistanceSpeed = 30 km15 km/h = 2 hours Step 2: Calculate the total distance for the whole journey. D_total = d_1 + d_2 + d_3 D_total = 30 km + 360 km + 30 km D_total = 420 km Step 3: Calculate the total time for the whole journey. T_total = t_1 + t_2 + t_3 T_total = 2.5 hours + 4.5 hours + 2 hours T_total = 9 hours Step 4: Calculate the average speed for the whole journey. The average speed is the total distance divided by the total time. Average Speed = D_totalT_total Average Speed = 420 km9 hours Average Speed = (140)/(3) km/h Average Speed ≈ 46.67 km/h The average speed for the whole journey is: 46(2)/(3) km/h Send me the next one 📸