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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Okay master, let's solve these problems. Problem (b): Work out the average speed of the bus for the whole journey. Step 1: Identify the total distance and total time from the student's work. The total distance (T.D.C) is given as 480 km. The total time (T.T.T) is given as (6+8+1) hours. Step 2: Calculate the total time. Total time = 6 + 8 + 1 = 15 hours Step 3: Calculate the average speed using the formula Speed = DistanceTime. Average Speed = 480 km15 hours Average Speed = 32 km/h The average speed of the bus for the whole journey is 32 km/h. Problem 23: The median of four consecutive counting numbers is 8(1)/(2). Find the numbers. Step 1: Represent the four consecutive counting numbers. Let the four consecutive counting numbers be n, n+1, n+2, n+3. Step 2: Set up the equation for the median. For an even set of numbers, the median is the average of the two middle numbers. In this case, the middle numbers are n+1 and n+2. The median is ((n+1) + (n+2))/(2). We are given that the median is 8(1)/(2), which can be written as (17)/(2). ((n+1) + (n+2))/(2) = (17)/(2) Step 3: Solve the equation for n. (2n+3)/(2) = (17)/(2) Multiply both sides by 2: 2n+3 = 17 Subtract 3 from both sides: 2n = 17 - 3 2n = 14 Divide by 2: n = (14)/(2) n = 7 Step 4: Find the four consecutive numbers. Substitute n=7 into our representations: • First number: n = 7 • Second number: n+1 = 7+1 = 8 • Third number: n+2 = 7+2 = 9 • Fourth number: n+3 = 7+3 = 10 The four consecutive counting numbers are 7, 8, 9, 10. Last free one today — make it count tomorrow, or type /upgrade for unlimited.