Final answer:
The problem can be solved using algebra to set up two equations representing the distance traveled at the usual speed and the increased speed. After substituting values, we solve for the usual speed V, which is crucial for the airplane to reach its destination on time, despite the delay.
Step-by-step explanation:
To solve the problem of finding the aeroplane's usual speed, we will use the basic concepts of speed, time, and distance. Let's denote the plane's usual speed as V, and the increased speed as V + 250 km/hr. Since the plane left 30 minutes (or 0.5 hours) late, it needs to cover 1500 km in a time that is 0.5 hours less than it usually would.
Under normal conditions, the travel time (T) at the usual speed is given by:
T = distance / usual speed = 1500 km / V
With the increased speed, the time (T - 0.5) to cover the same distance is:
T - 0.5 = 1500 km / (V + 250)
Now we have two equations:
- 1500 km = T * V
- 1500 km = (T - 0.5) * (V + 250)
By substituting T from the first equation into the second, we get:
1500 km = (1500 km / V - 0.5) * (V + 250)
This equation can then be solved for V, which is the aeroplane's usual speed.
To solve the equation, first distribute the term on the right side:
1500 km = 1500 km + (1500 km * 250) / V - (0.5 * V) - (0.5 * 250)
The terms 1500 km cancel out on both sides, and then you can solve for V.
The usual speed V is essential to ensure that the aeroplane reaches its destination on time despite the delay.