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
Step 1: Calculate the distance Wafula covered before Nekesa started. Wafula started at 8:00 am. Nekesa started at 8:21 am. Time difference = 8:21 am - 8:00 am = 21 minutes. Convert minutes to hours: 21 minutes = (21)/(60) hours = (7)/(20) hours Wafula's speed = 90 km/hr. Distance covered by Wafula = Speed × Time D_W = 90 km/hr × (7)/(20) hr = (90 × 7)/(20) km = (9 × 7)/(2) km = (63)/(2) km = 31.5 km This is the head start distance Wafula has. Step 2: Calculate the relative speed of Nekesa with respect to Wafula. Both are moving in the same direction. Nekesa's speed = 97 km/hr. Wafula's speed = 90 km/hr. Relative speed = Nekesa's speed - Wafula's speed V_relative = 97 km/hr - 90 km/hr = 7 km/hr Step 3: Calculate the time it takes for Nekesa to catch up with Wafula. Time to catch up = Head start distance / Relative speed T_catch-up = 31.5 km7 km/hr = 4.5 hours Convert 0.5 hours to minutes: 0.5 × 60 = 30 minutes. So, the time to catch up is 4 hours and 30 minutes. Step 4: Determine the time Nekesa caught up with Wafula. Nekesa started at 8:21 am. Catch-up time = Nekesa's start time + Time to catch up 8:21 am + 4 hours 30 minutes 8:21 am + 4 hours = 12:21 pm 12:21 pm + 30 minutes = 12:51 pm The time Nekesa caught up with Wafula is 12:51 pm. Send me the next one 📸