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
Hey blessed — ready when you are. The problem describes two vehicles traveling from one town to another. We need to determine when the saloon car catches up with the bus. Step 1: Calculate the distance the bus traveled before the saloon car started. The bus traveled for 40 minutes at a speed of 60 km/h. First, convert 40 minutes to hours: 40 minutes = (40)/(60) hours = (2)/(3) hours Distance covered by the bus in 40 minutes: Distance = Speed × Time Distance_bus initial = 60 km/h × (2)/(3) h = 40 km Step 2: Determine the relative speed of the saloon car with respect to the bus. Both vehicles are moving in the same direction. Speed of the bus (V_B) = 60 km/h Speed of the saloon car (V_S) = 80 km/h Relative speed (V_R) = V_S - V_B V_R = 80 km/h - 60 km/h = 20 km/h Step 3: Calculate the time it takes for the saloon car to catch up with the bus. The saloon car needs to cover the initial distance of 40 km that the bus traveled. Time = DistanceRelative Speed Time_catch up = 40 km20 km/h = 2 hours Step 4: Calculate the distance from Nakuru where the saloon car catches up with the bus. The saloon car travels for 2 hours at a speed of 80 km/h. Distance_catch up = Speed_saloon car × Time_catch up Distance_catch up = 80 km/h × 2 h = 160 km The saloon car catches up with the bus at a distance of 160 km from Nakuru. The total distance between the towns is 320 km. The question asks "How far from Nakuru did the saloon car catch up with the bus?". The saloon car caught up with the bus at a distance of 160 km. Send me the next one 📸