Calculate, for the entire journey, the average speed of the shuttle.

Welcome back — been a while! Let's pick up where you left off. a) Calculate, for the entire journey, the average speed of the shuttle. Step 1: Determine the distance for each half of the journey and the time taken for each half. The total distance is 300 km. The distance for the first half is D_1 = 300 km2 = 150 km. The speed for the first half is v_1 = 60 km/h. The time taken for the first half is T_1 = (D_1)/(v_1). T_1 = 150 km60 km/h = 2.5 hours The distance for the second half is D_2 = 300 km2 = 150 km. The speed for the second half is v_2 = 90 km/h. The time taken for the second half is T_2 = (D_2)/(v_2). T_2 = 150 km90 km/h = (15)/(9) hours = (5)/(3) hours Step 2: Calculate the total time for the entire journey. The total time T_total is the sum of the times for the first and second halves. T_total = T_1 + T_2 = 2.5 h + (5)/(3) h = (5)/(2) h + (5)/(3) h To add these fractions, find a common denominator, which is 6. T_total = (5 × 3)/(2 × 3) h + (5 × 2)/(3 × 2) h = (15)/(6) h + (10)/(6) h = (25)/(6) hours Step 3: Calculate the average speed for the entire journey. The average speed v_avg is the total distance divided by the total time. v_avg = Total DistanceTotal Time = 300 km(25)/(6) h v_avg = 300 km × (6)/(25 h) = (1800)/(25) km/h = 72 km/h The average speed for the entire journey is 72 km/h. b) If the speed of the shuttle in the first half of the journey is reduced to 50 km/h, determine its effect on the overall time. Step 1: Calculate the new time for the first half of the journey. The distance for the first half remains D_1 = 150 km. The new speed for the first half is v'_1 = 50 km/h. The new time taken for the first half is T'_1 = (D_1)/(v'_1). T'_1 = 150 km50 km/h = 3 hours Step 2: Calculate the new total time for the journey. The time for the second half remains T_2 = (5)/(3) hours (from part a). The new total time T'_total is the sum of the new time for the first half and the time for the second half. T'_total = T'_1 + T_2 = 3 h + (5)/(3) h T'_total = (9)/(3) h + (5)/(3) h = (14)/(3) hours Step 3: Determine the effect on the overall time by comparing the new total time with the original total time. The original total time was T_total = (25)/(6) hours (from part a). The change in overall time is T = T'_total - T_total. T = (14)/(3) h - (25)/(6) h To subtract these fractions, find a common denominator, which is 6. T = (14 × 2)/(3 × 2) h - (25)/(6) h = (28)/(6) h - (25)/(6) h = (3)/(6) h = (1)/(2) hour To express this in minutes: (1)/(2) h × 60 min/h = 30 minutes The overall time increases by 30 minutes. Send me the next one 📸