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
Let's solve this problem step by step. First, we need to clarify some details. The problem states "sixty minutes after starting the journey he made a step to cooltown and reached datanu 60 minutes later." This means: Time at Cooltown = 60 minutes from start. Time at Datanu = 60 minutes (to Cooltown) + 60 minutes (Cooltown to Datanu) = 120 minutes from start. Total distance to Datanu = 40 km. The distance to Cooltown is not explicitly given. For the purpose of drawing a distance-time graph and solving the subsequent parts, we will assume Adamu traveled at a constant speed throughout his journey. This means that at 60 minutes (half the total time), he would have covered half the total distance (20 km). Therefore, Cooltown is 20 km from Kadumgu. A) Using a scale of 2cm to 2 units on the horizontal axis and 2cm to 5km on the vertical axis, draw a distance time graph for Adamu to make the whole journey. Step 1: Determine the scales for the axes. Horizontal axis (Time): 2 cm = 2 minutes ⟹ 1 cm = 1 minute. Vertical axis (Distance): 2 cm = 5 km ⟹ 1 cm = 2.5 km. Step 2: Identify the key points for the journey based on our assumption. Start (Kadumgu): (Time = 0 minutes, Distance = 0 km) Cooltown: (Time = 60 minutes, Distance = 20 km) End (Datanu): (Time = 120 minutes, Distance = 40 km) Step 3: Describe how to draw the graph. Draw a horizontal axis labeled "Time (minutes)" and a vertical axis labeled "Distance (km)". Mark the horizontal axis in increments of 10 or 20 minutes (e.g., 0, 20, 40, 60, 80, 100, 120 minutes), ensuring 1 cm represents 1 minute. Mark the vertical axis in increments of 5 or 10 km (e.g., 0, 10, 20, 30, 40 km), ensuring 1 cm represents 2.5 km. Plot the points: (0, 0), (60, 20), and (120, 40). Draw a straight line* connecting these three points. This line represents Adamu's journey. B) Using the graph to determine the; i) distance from cooltown to adamu Step 1: Locate Cooltown on the graph. This is the point where time is 60 minutes. Step 2: Read the corresponding distance value on the vertical axis. The distance from Kadumgu (Adamu's starting point) to Cooltown is 20 km*. ii) total time (in minutes), taken by adamu to make the whole journey. Step 1: Identify the start and end times of the journey. Journey started at 0 minutes. Journey ended when Adamu reached Datanu. The problem states he reached Datanu 60 minutes after reaching Cooltown, which was 60 minutes after starting. Step 2: Calculate the total time. Total time = 60 minutes + 60 minutes = 120 minutes*. iii) average speed of adamu from cooltown to datanu. Step 1: Determine the distance traveled from Cooltown to Datanu. Distance to Datanu = 40 km. Distance to Cooltown = 20 km. Distance from Cooltown to Datanu = 40 km - 20 km = 20 km. Step 2: Determine the time taken from Cooltown to Datanu. Time at Datanu = 120 minutes. Time at Cooltown = 60 minutes. Time taken = 120 minutes - 60 minutes = 60 minutes. Step 3: Convert time to hours for speed calculation (km/h). 60 minutes = 1 hour. Step 4: Calculate the average speed using the formula: Speed = Distance / Time. Average speed = 20 km / 1 hour = 20 km/h*. C) If adamu did not rest but traveled to datanu within the time what was his average speed Step 1: Identify the total distance and total time for the entire journey. Total distance = 40 km. Total time = 120 minutes. Step 2: Convert total time to hours. 120 minutes = 2 hours. Step 3: Calculate the overall average speed using the formula: Average Speed = Total Distance / Total Time. Average speed = 40 km / 2 hours = 20 km/h*. 3 done, 2 left today. You're making progress.