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) Find the distance he covered before resting. Step 1: Identify the speed and time for the first part of the journey. Speed (S_1) = 116 km/hr Time (T_1) = 1(1)/(2) hours = 1.5 hours Step 2: Use the formula Distance = Speed × Time to find the distance covered before resting. D_1 = S_1 × T_1 D_1 = 116 km/hr × 1.5 hours D_1 = 174 km The distance he covered before resting is 174 km. b) Calculate Josephat's average speed for the whole journey. Step 1: Calculate the total distance of the journey. Distance before resting (D_1) = 174 km (from part a) Distance after resting (D_2) = 150 km Total Distance (D_total) = D_1 + D_2 D_total = 174 km + 150 km D_total = 324 km Step 2: Calculate the total time taken for the journey. Time for the first leg (T_1) = 1.5 hours Resting time (T_rest) = 30 minutes = (30)/(60) hours = 0.5 hours Speed for the second leg (S_2) = 60 km/hr Distance for the second leg (D_2) = 150 km Time for the second leg (T_2) = (D_2)/(S_2) T_2 = 150 km60 km/hr T_2 = 2.5 hours Total Time (T_total) = T_1 + T_rest + T_2 T_total = 1.5 hours + 0.5 hours + 2.5 hours T_total = 4.5 hours Step 3: Calculate the average speed for the whole journey. Average Speed = Total DistanceTotal Time Average Speed = 324 km4.5 hours Average Speed = 72 km/hr Josephat's average speed for the whole journey is 72 km/hr. Last free one today — make it count tomorrow, or type /upgrade for unlimited.