An aeroplane flew 30km due North from point A to point B and then flew another 40km due East from point B to point C. The total time taken for the aeroplane to fly from point A to point C is 14 hours.
A. Correctly draw a diagram to illustrate the above information.
B. What is the average speed of the aeroplane in flying from point A to B to C?
C. Calculate the distance from point A directly to point C.
D. How long will the aeroplane take to fly directly from point C to point A, if it flies at the same average speed?
E. The aeroplane uses 2L fuel per hour. If the cost of fuel is k4. 50 per liter, what will be the cost of the fuel needed to travel from A to B to C and back to A again?
A. Diagram:
C
/ |
/ |
/ |
40km / | 30km
/ |
/ |
/________|
A B
B. Average speed = Total distance / Total time taken
= (30km + 40km) / 14 hours
= 70km / 14 hours
= 5km/h
C. Distance from A to C can be calculated using Pythagoras' theorem:
AC^2 = AB^2 + BC^2
AC^2 = 30^2 + 40^2
AC^2 = 900 + 1600
AC^2 = 2500
AC = √2500
AC = 50km
D. Time taken to fly directly from C to A at the same average speed:
Time = Distance / Speed
Time = 50km / 5km/h
Time = 10 hours
E. Total distance travelled in going from A to B to C and back to A = 30km + 40km + 50km + 50km = 170km
Total fuel needed = 170km / 2L = 85L
Cost of fuel = 85L * k4.50 = k382.50