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
Here's the solution to the problem: 19. (a) Matatu and Police Car Matatu speed (S_M) = 99 km/h Police car speed (S_P) = 132 km/h Matatu passes checkpoint at 9:00 a.m. Police car passes checkpoint at 9:15 a.m. i) The relative speed of the two vehicles Step 1: Calculate the difference in speeds since both vehicles are moving in the same direction. Relative speed = S_P - S_M Relative speed = 132 km/h - 99 km/h Relative speed = 33 km/h ii) The distance between the two vehicles as at 9:15 a.m. Step 1: Determine the time the matatu has traveled before the police car starts from the checkpoint. Time elapsed = 9:15 a.m. - 9:00 a.m. = 15 minutes Step 2: Convert the time to hours. Time in hours = (15)/(60) h = 0.25 h Step 3: Calculate the distance covered by the matatu in this time. Distance = S_M × Time Distance = 99 km/h × 0.25 h Distance = 24.75 km iii) The time the police car will overtake the matatu. Step 1: Use the distance between the vehicles at 9:15 a.m. and their relative speed to find the time to overtake. Time to overtake = Distance between vehiclesRelative speed Time to overtake = 24.75 km33 km/h Time to overtake = 0.75 hours Step 2: Convert the time to minutes. Time to overtake = 0.75 × 60 minutes = 45 minutes Step 3: Add this time to the police car's start time (when it passed the checkpoint). Overtaking time = 9:15 a.m. + 45 minutes Overtaking time = 10:00 a.m. 19. (b) Two Passenger Trains Initial distance between trains = 240 m Train A speed (S_A) = 164 km/h Train B speed (S_B) = 88 km/h Train A length (L_A) = 150 m Train B length (L_B) = 100 m Step 1: Calculate the relative speed of the trains. Since they are approaching each other, their speeds add up. Relative speed = S_A + S_B Relative speed = 164 km/h + 88 km/h = 252 km/h Step 2: Convert the relative speed from km/h to m/s. Relative speed = 252 km/h × 1000 m1 km × 1 h3600 s Relative speed = 252 × (5)/(18) m/s = 70 m/s Step 3: Calculate the total distance the trains must cover to completely pass each other. This includes the initial distance between them and their combined lengths. Total distance = Initial distance + L_A + L_B Total distance = 240 m + 150 m + 100 m = 490 m Step 4: Determine the time taken for the trains to completely pass each other. Time = Total distanceRelative speed Time = 490 m70 m/s Time = 7 seconds That's 2 down. 3 left today — send the next one.