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.
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Here are the solutions to the problems: 23. A motorist started a journey at 8:30 am, travelling at 120 km/hr and covered a distance of 240 km. a) Calculate the time he took. Step 1: Identify the given values and the formula. Speed = 120 km/hr Distance = 240 km Time = DistanceSpeed Step 2: Substitute the values into the formula. Time = 240 km120 km/hr Step 3: Calculate the time. Time = 2 hours The time he took is 2 hours. b) At what time did he finish the journey? Step 1: Identify the start time and the duration of the journey. Start time = 8:30 am Duration = 2 hours Step 2: Add the duration to the start time. 8:30 am + 2 hours = 10:30 am He finished the journey at 10:30 am. 24. Given that a=4, b=2 and c=3. Find the value of: i) abc Step 1: Substitute the given values into the expression. abc = 4 × 2 × 3 Step 2: Multiply the numbers. abc = 8 × 3 abc = 24 The value of abc is 24. ii) (ac)/(b) Step 1: Substitute the given values into the expression. (ac)/(b) = (4 × 3)/(2) Step 2: Multiply the numbers in the numerator. (ac)/(b) = (12)/(2) Step 3: Divide the numbers. (ac)/(b) = 6 The value of (ac)/(b) is 6. iii) a^2 Step 1: Substitute the given value of a into the expression. a^2 = 4^2 Step 2: Calculate the square. a^2 = 4 × 4 a^2 = 16 The value of a^2 is 16. 25. The sum of three consecutive odd numbers is 39. Find the numbers. Step 1: Let the first odd number be x. The next consecutive odd number is x+2. The third consecutive odd number is x+4. Step 2: Set up the equation based on the given sum. x + (x+2) + (x+4) = 39 Step 3: Combine like terms. 3x + 6 = 39 Step 4: Subtract 6 from both sides of the equation. 3x = 39 - 6 3x = 33 Step 5: Divide by 3 to solve for x. x = (33)/(3) x = 11 Step 6: Find the three consecutive odd numbers. First number: x = 11 Second number: x+2 = 11+2 = 13 Third number: x+4 = 11+4 = 15 The three consecutive odd numbers are 11, 13, 15.