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 question 23: a) i) The time of the day the two vehicles met: Step 1: Calculate the head start time for the bus. The bus leaves at 0815 hours. The car leaves at 1035 hours. Head start time = 1035 - 0815 = 2 hours 20 minutes Convert minutes to hours: 20 minutes = (20)/(60) hours = (1)/(3) hours. Head start time = 2 + (1)/(3) hours = (7)/(3) hours Step 2: Calculate the distance covered by the bus during its head start. Distance covered by bus = Speed of bus × Head start time Distance covered by bus = 90 km/h × (7)/(3) hours = 210 km Step 3: Calculate the remaining distance when the car starts. Remaining distance = Total distance - Distance covered by bus Remaining distance = 760 km - 210 km = 550 km Step 4: Calculate the relative speed of the two vehicles. Since they are moving towards each other, their speeds add up. Relative speed = Speed of bus + Speed of car Relative speed = 90 km/h + 110 km/h = 200 km/h Step 5: Calculate the time taken for them to meet after the car starts. Time to meet = Remaining distanceRelative speed Time to meet = 550 km200 km/h = (11)/(4) hours Convert this time to hours and minutes: (11)/(4) hours = 2 34