In a flight of 600 km , an aircraft was slowed down due to bad weather The average speed - Maths - Some Applications of Trigonometry

Question

In a flight of 600 km , an aircraft was slowed down due to bad
weather The average speed for the trip was decreased by 200 km/h
& the time of flight increased by 30 minutes Find the duration
of flight

Aakash Sharma · Accepted Answer

Let the usual speed of the plane be x km/hr.

Reduced speed of the plane = (x – 200) km/hr

Time taken to reach the destination at usual speed, $t_{1} = \frac{600}{x} hr$

Time taken to reach the destination at reduced speed, $t_{2} = \frac{600}{x - 200} hr$

Given, t ₂ – t ₁ = 30 min

We know that 60 minutes = 1 hour

Therefore, 30 minutes = 30/60 hour = 1/2 hour

$∴ \frac{600}{x - 200} h r - \frac{600}{x} h r = 30 \min \Rightarrow \frac{600}{x - 200} h r - \frac{600}{x} h r = \frac{1}{2} h r$

$\Rightarrow \frac{600 x - 600 x + 120000}{x (x - 200)} = \frac{1}{2} [o n t a k i n g L C M] \Rightarrow x^{2} - 200 x = 240000 \Rightarrow x^{2} - 200 x - 240000 = 0 \Rightarrow x^{2} - 600 x + 400 x - 240000 = 0 \Rightarrow x (x - 600) + 400 (x - 600) = 0 \Rightarrow (x - 600) (x + 400) = 0 \Rightarrow x - 600 = 0 or x + 400 = 0 \Rightarrow x = 600 or x = - 400 ∴ x = 600 (∵ Speed cannot be negative)$

Duration of the flight $= (\frac{600}{x} + \frac{30}{60}) h r = (\frac{600}{600} + \frac{1}{2}) h r = (1 + \frac{1}{2}) h r = \frac{3}{2} h r$

Thus, the duration of the flight is $\frac{3}{2} h r$ .

76

In a flight of 600 km , an aircraft was slowed down due to bad weather. The average speed for the trip was decreased by 200 km/h & the time of flight increased by 30 minutes. Find the duration of flight.