In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

Question

The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:

Answer 1

Step 1: Let Usual Speed be x
Distance = 600 km

Usual time:
t₁ = 600 / x

Reduced speed = x − 200
New time:
t₂ = 600 / (x − 200)

Given:
t₂ − t₁ = 0.5 hours

Step 2: Form the Equation
600/(x − 200) − 600/x = 1/2

Take LCM:
600x − 600(x − 200) / x(x − 200) = 1/2

Simplify numerator:
600x − 600x + 120000
= 120000

So equation becomes:
120000 / x(x − 200) = 1/2

Step 3: Cross Multiply
240000 = x(x − 200)

x² − 200x − 240000 = 0

Factorise:
x² − 600x + 400x − 240000 = 0
(x − 600)(x + 400) = 0

x = 600 or x = −400

Speed cannot be negative,
x = 600 km/h

Step 4: Find Scheduled Duration
Scheduled time = 600 / 600
= 1 hour

Final Answer:
Scheduled duration of the flight = 1 hour

In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

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Solution and Explanation

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