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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Question 4: Step 1: Find the least common multiple (LCM) of the times Diana and Rahima take to complete one round. This will be the time after which they meet again at the starting point. Diana's time = 48 minutes Rahima's time = 36 minutes Prime factorization of 48: 48 = 2 × 24 = 2 × 2 × 12 = 2 × 2 × 2 × 6 = 2^4 × 3^1 Prime factorization of 36: 36 = 2 × 18 = 2 × 2 × 9 = 2^2 × 3^2 Step 2: Calculate the LCM of 48 and 36. LCM(48, 36) = 2^(4,2) × 3^(1,2) = 2^4 × 3^2 = 16 × 9 = 144 minutes Step 3: Convert the total time in minutes to hours and minutes. 144 minutes = (144)/(60) hours = 2 hours and 24 minutes (Since 2 × 60 = 120, and 144 - 120 = 24) Step 4: Add this time to the starting time to find when they will meet again. Starting time = 8:06 a.m. Time to meet again = 2 hours 24 minutes Meeting time = 8:06 a.m. + 2 hours 24 minutes = 10:30 a.m. They will meet again at the starting point at 10:30 a.m. Question 5: There is no question 5 visible in the image provided. Last free one today — make it count tomorrow, or type /upgrade for unlimited.