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
a) To draw the distance-time graph for the cyclist: Step 1: Determine the coordinates for each segment of the journey. • Segment 1: From A to B Start time: 6:30 am End time: 7:00 am Duration: 7:00 am - 6:30 am = 30 minutes Distance covered: 12 km Point 1: (6:30 am, 0 km) Point 2: (7:00 am, 12 km) • Segment 2: Stop at B Start time: 7:00 am Duration of stop: 1(1)/(2) hours = 1 hour 30 minutes End time of stop: 7:00 am + 1 hour 30 minutes = 8:30 am Distance covered: 0 km (distance remains 12 km) Point 3: (8:30 am, 12 km) • Segment 3: From B to C Start time: 8:30 am Starting distance: 12 km Destination C is 20 km away. Distance to cover: 20 km - 12 km = 8 km Speed: 16 km/h Time taken: Time = DistanceSpeed = 8 km16 km/h = 0.5 hours = 30 minutes End time: 8:30 am + 30 minutes = 9:00 am End distance: 20 km Point 4: (9:00 am, 20 km) Step 2: Set up the graph axes according to the given scale. • Vertical axis (Distance): 2 cm represents 4 km. If each grid square is 1 cm, then 2 squares represent 4 km. Label the axis from 0 km to 20 km (e.g., 0, 4, 8, 12, 16, 20). • Horizontal axis (Time): 2 cm represents 30 minutes. If each grid square is 1 cm, then 2 squares represent 30 minutes. Label the axis starting from 6:30 am (e.g., 6:30 am, 7:00 am, 7:30 am, 8:00 am, 8:30 am, 9:00 am). Step 3: Plot the points and draw the graph. 1. Plot the starting point: (6:30 am, 0 km). 2. Draw a straight line from (6:30 am, 0 km) to (7:00 am, 12 km). 3. Draw a horizontal line from (7:00 am, 12 km) to (8:30 am, 12 km) to represent the stop. 4. Draw a straight line from (8:30 am, 12 km) to (9:00 am, 20 km). b) To find the time taken for the cyclist to reach the destination using the graph: Step 1: Locate the destination distance on the vertical axis. The destination is 20 km. Find 20 km on the vertical axis. Step 2: Read the corresponding time on the horizontal axis. Follow horizontally from 20 km to the graph line, then vertically down to the time axis. This point corresponds to 9:00 am. Step 3: Calculate the total time taken. The journey started at 6:30 am and ended at 9:00 am.