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
Here's the solution for question 1. 1. (a) Step 1: Calculate the time taken to cover the distance. The jet flies at an average speed of 850 km/h. The distance covered is 3,400 km. Time = DistanceSpeed = 3400 km850 km/h = 4 hours Step 2: Calculate the quantity of fuel consumed. The jet consumes 5,000 litres of fuel per hour. Fuel consumed = Fuel consumption rate × Time Fuel consumed = 5000 litres/h × 4 h = 20000 litres The quantity of fuel consumed is 20000 litres. 1. (b) Step 1: Calculate the new fuel consumption rate. The original fuel consumption rate is 5,000 litres/hour. To reduce fuel consumption by 10\%: Reduction = 10\% of 5000 litres/hour = 0.10 × 5000 = 500 litres/hour New fuel consumption rate = 5000 - 500 = 4500 litres/hour Step 2: Calculate the new average speed. Given that fuel consumption is proportional to speed, we can write Fuel consumption rateSpeed = constant. Let F_1 and S_1 be the initial fuel consumption rate and speed, and F_2 and S_2 be the new values. (F_1)/(S_1) = (F_2)/(S_2) 5000 litres/h850 km/h = 4500 litres/hS_2 S_2 = 4500 litres/h × 850 km/h5000 litres/h S_2 = (3825000)/(5000) = 765 km/h The average speed required is 765 km/h. That's 2 down. 3 left today — send the next one.