Due to bad weather, a flight was slowed down and as a result, its average speed of the trip was reduced by 400 km/hr and the time of flight increased by 3 hours. What is the actual duration of the flight if the flight covers a distance of 2400 km?

Due to bad weather, a flight was slowed down and as a result, its average speed of the trip was reduced by 400 km/hr and the time of flight increased by 3 hours. What is the actual duration of the flight if the flight covers a distance of 2400 km? Correct Answer 3 hours

Short trick:

Let the initial speed be x km/hr.

Using formula, d = xy/(x – y) × Δt

2400 = x(x – 400)/400 × 3

x(x – 400) = 800 × 400

⇒ x = 800

∴ Actual duration = 2400/800 = 3 hr

Detailed solution:

Let the duration of the flight is y hours

Now,

⇒ Speed of the flight = 2400/y

⇒ Speed of the flight after bad weather = 2400/(y + 3)

We know, the speed reduced by 400 km/h due to bad weather,

⇒ (2400/y) – {2400/(y + 3)} = 400

⇒ (6/y) – {6/(y + 3)} = 1

⇒ y² + 3y – 18 = 0

⇒ y = -6, 3

As. time cannot be negative so -6 not a valid value.

⇒ y = 3