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: <br /><br />Let's understand this problem gradually.<br /><br />1. The Scale: It is given that 1 cm on the scale map equals 125 km on land.<br />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.<br /><br />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.<br /><br />Mathematical Expression 1: <br /><br />Distance on map = 11.6 cm.<br /><br />Each cm represents 125 km.<br /><br />Actual distance \( = 11.6 \times 125 \) applying the conversion from cm to km by the scale.<br /><br />Next step necessitates the calculation of the total time spent on the flight. <br /><br />Given, plane departed at 0947 and arrived at 1207. <br /><br />So overall:<br /><br />0947 ➝ 1000 equals 13 minutes <br /><br />1000 ➝ 1200 equals 120 minutes <br /><br />1200 ➝ 1207 equal 7 minutes<br /><br />By adding all these sections up, you will then compute the total time in minutes.<br /><br />Once done, we then will convert the total flight time in minutes to hours since speed is being asked in kilometers per hour.<br /><br />Finally, the speed of the plane could be calculated by dividing the total flight distance by the total flight time.<br /><br /><br />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:<br /><br />Mathematical Expression 2:<br /><br />Departure time = 0947 <br /><br />Arrival time = 1207<br /><br />Total Duration (minutes) \( = (13 + 120 + 7) \)<br /><br />Total Duration (hours) \( = Divide~’Total Duration (minutes)’~by~60 \)<br /><br />Finally,<br /><br />Mathematical Expression 3: <br /><br />Average Speed = Actual distance ÷ Duration(in hours)<br /><br /><br /><br />Detailed Calculation:<br /><br />1. Using expression 1:<br /><br /> Actual distance \( = 11.6 \times 125 = 1450 km \)<br /><br />2. For the travel time with expression 2:<br /><br /> Total Flight Duration \( = (13+120+7) = 140 minutes \)<br /><br /> Converting the minutes into hours:<br /><br /> Total Flight Duration (in Hours) \( = 140 ÷ 60 = 2.33 hours \)<br /><br />3. And the speed by expression 3:<br /><br /><br /> Average Speed \( = 1450 ÷ 2.33 = 623.36 km/h \)<br /><br /><br />Conclusion: <br /><br />Therefore, the airplane's average speed was in fact approximately \( \boxed{623.36} \) kilometers per hour.