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The distance between Delhi and Chennai by flight is 1600 km. An aircraft was slowed down due to bad weather. The time of journey of Chennai from Delhi is increased by 40 minutes and the average speed for the journey was reduced by 200 km/h. What is the usual duration of the flight if there is no bad weather?

The distance between Delhi and Chennai by flight is 1600 km. An aircraft was slowed down due to bad weather. The time of journey of Chennai from Delhi is increased by 40 minutes and the average speed for the journey was reduced by 200 km/h. What is the usual duration of the flight if there is no bad weather? Correct Answer 120 minutes

Let T be the usual duration(hours) of flight.

Usual speed of the flight = 1600/T

Due to bad weather, speed of the flight = 1600/(T + 40/60) = 1600/(T + 2/3)

Now, according to question, 1600/T - 1600/(T + 2/3) = 200

⇒ 1/T - 1/(T + 2/3) = 200/1600 = 1/8

⇒ (2/3)/(T2 + 2T/3) = 1/8

⇒ 2/(3T2 + 2T) = 1/8

⇒ 3T2 + 2T = 16

⇒ 3T2 + 2T – 16 = 0

⇒ 3T2 - 6T + 8T – 16 = 0

⇒ (3T + 8) × (T – 2) = 0

⇒ T = -8/3 or 2

⇒ T = 2 hours = 120 minutes  

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