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
1. Find correct to two significant figures the walking speed Step 1: Define variables and convert units. Let v_w be the walking speed in km/h. Let v_c be the cycling speed in km/h. Cycling time t_c = 45 minutes = (45)/(60) hours = (3)/(4) hours. Walking time t_w = 1 hour. Total distance D_total = 10.4 km. Given that v_c = 3v_w. Step 2: Set up equations for distances. Distance cycled D_c = v_c × t_c = (3v_w) × (3)/(4) = (9)/(4) v_w. Distance walked D_w = v_w × t_w = v_w × 1 = v_w. Step 3: Solve for the walking speed. The total distance is the sum of the distances cycled and walked: D_c + D_w = D_total (9)/(4) v_w + v_w = 10.4 (9)/(4) v_w + (4)/(4) v_w = 10.4 (13)/(4) v_w = 10.4 v_w = (10.4 × 4)/(13) v_w = (41.6)/(13) v_w = 3.2 km/h The walking speed, correct to two significant figures, is 3.2 km/h. 2. If Mabel increase the average cycling speed by 20% but maintain the walking speed for 1 hours find in minutes the new cycling time Step 1: Calculate the original cycling speed and the new cycling speed. Original walking speed v_w = 3.2 km/h. Original cycling speed v_c = 3v_w = 3 × 3.2 = 9.6 km/h. New cycling speed v_c' = v_c × (1 + 0.20) = 9.6 × 1.20 = 11.52 km/h. Step 2: Calculate the distance walked and the remaining distance to be cycled. Walking speed is maintained at v_w = 3.2 km/h. Walking time is maintained at t_w = 1 hour. Distance walked D_w = v_w × t_w = 3.2 km/h × 1 h = 3.2 km. Total distance remains 10.4 km. Distance to be cycled D_c' = D_total - D_w = 10.4 km - 3.2 km = 7.2 km. Step 3: Calculate the new cycling time in minutes. New cycling time t_c' = (D_c')/(v_c') = 7.2 km11.52 km/h = 0.625 hours. Convert to minutes: t_c' = 0.625 hours × 60 minutes/hour t_c' = 37.5 minutes The new cycling time is 37.5 minutes. What's next?