The scale diagram below shows two cities, P and Q. square 125 km P. A plane departs from Pat 0947 and arrives at Q at 1207. Work out the average speed, in kilometres per hour, of the plane. Note: the distance between P and Q on the map is 11.6 cm. (5 marks)

Explanation: Let's understand this problem gradually.1. The Scale: It is given that 1 cm on the scale map equals 125 km on land.2. Flight distance and time: The plane travels a distance represented by 11.6 cm on the map from city P to city Q. The departure time is 0947 and the arrival time at destination Q is 1207.The first step in assessing the problem is to convert the distance measured on the map to the actual distance in kilometers, as guided by the given scale.Mathematical Expression 1: Distance on map = 11.6 cm.Each cm represents 125 km.Actual distance applying the conversion from cm to km by the scale.Next step necessitates the calculation of the total time spent on the flight. Given, plane departed at 0947 and arrived at 1207. So overall:0947 ➝ 1000 equals 13 minutes 1000 ➝ 1200 equals 120 minutes 1200 ➝ 1207 equal 7 minutesBy adding all these sections up, you will then compute the total time in minutes.Once done, we then will convert the total flight time in minutes to hours since speed is being asked in kilometers per hour.Finally, the speed of the plane could be calculated by dividing the total flight distance by the total flight time.Avoid quickly jumping through different parts of calculations, let's note down the above steps in mathematical formulas and start to perform the suggested calculations:Mathematical Expression 2:Departure time = 0947 Arrival time = 1207Total Duration (minutes) \( = (13 + 120 + 7) \)Total Duration (hours) \( = Divide~’Total Duration (minutes)’~by~60 \)Finally,Mathematical Expression 3: Average Speed = Actual distance ÷ Duration(in hours)Detailed Calculation:1. Using expression 1: Actual distance 2. For the travel time with expression 2: Total Flight Duration \( = (13+120+7) = 140 minutes \) Converting the minutes into hours: Total Flight Duration (in Hours) 3. And the speed by expression 3: Average Speed Conclusion: Therefore, the airplane's average speed was in fact approximately kilometers per hour.