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's the solution to question 16. Part i: The time taken before the two friends met. Step 1: Calculate the duration of Ojiwang's head start. Ojiwang started at 9:00 a.m. David started at 10:30 a.m. The time difference is 10:30 a.m. - 9:00 a.m. = 1 hour 30 minutes = 1.5 hours. Step 2: Calculate the distance Ojiwang covered during his head start. Ojiwang's speed is 15 km/h. Distance = Speed × Time D_Ojiwang initial = 15 km/h × 1.5 h = 22.5 km Step 3: Determine the remaining distance between them when David started cycling. The total distance between their houses is 40 km. D_remaining = 40 km - 22.5 km = 17.5 km Step 4: Calculate their relative speed. Since they are cycling towards each other, their speeds add up. Ojiwang's speed is 15 km/h. David's speed is 25 km/h. S_relative = 15 km/h + 25 km/h = 40 km/h Step 5: Calculate the time taken for them to meet after David started. Time = DistanceSpeed T_meet = D_remainingS_relative = 17.5 km40 km/h T_meet = (17.5)/(40) hours = (175)/(400) hours = (7)/(16) hours To convert this to minutes and seconds: (7)/(16) hours × 60 minutes/hour = (420)/(16) minutes = 26.25 minutes This is 26 minutes and 0.25 × 60 = 15 seconds. The time taken before the two friends met (after David started) is 26 minutes 15 seconds. Part ii: The time they met. Step 1: Add the meeting time duration to David's starting time. David started at 10:30 a.m. They met 26 minutes and 15 seconds later. Meeting Time = 10:30:00 a.m. + 00:26:15 Meeting Time = 10:56:15 a.m. The time they met is 10:56:15 a.m.. 3 done, 2 left today. You're making progress.