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 are the solutions to the questions based on the graph: IV) How many kilometers did he cover in the first 2 hours? Step 1: The journey started at 8:00 AM. The first 2 hours would be from 8:00 AM to 10:00 AM. Step 2: Looking at the graph, at 10:00 AM, the distance covered is 40 km. The cyclist covered: 40 km V) How long did he take to travel 50km? Step 1: From the graph, the cyclist covered the first 40 km in 2 hours (from 8:00 AM to 10:00 AM). Step 2: The remaining distance to reach 50 km is 50 km - 40 km = 10 km. Step 3: After a rest period, the cyclist resumed travel at 11:00 AM from 40 km. The speed during this final segment (from 11:00 AM to 12:00 PM) is calculated as: Speed = Distance coveredTime taken = 72 km - 40 km12:00 PM - 11:00 AM = 32 km1 hour = 32 km/h Step 4: Calculate the time taken to cover the remaining 10 km at this speed: Time = DistanceSpeed = 10 km32 km/h = (10)/(32) hours = (5)/(16) hours Step 5: Convert the fractional hours to minutes: (5)/(16) × 60 minutes = (300)/(16) minutes = 18.75 minutes Step 6: Add the time for the first 40 km and the time for the next 10 km to get the total travel time (excluding rest). Total travel time = 2 hours + 18.75 minutes. The cyclist took: 2 hours and 18.75 minutes VI) At what speed was the cyclist travelling between town P and town Q? Step 1: Town P is the starting point (0 km) and Town Q is the end point (72 km). Step 2: The total distance covered from Town P to Town Q is 72 km. Step 3: The total time elapsed from the start (8:00 AM) to the end (12:00 PM) is 4 hours. Step 4: Calculate the average speed for the entire journey: Average Speed = Total DistanceTotal Time = 72 km4 hours = 18 km/h The cyclist was travelling at an average speed of: 18 km/h What's next?