# in a flight of 2800km, an aircraft was slowed down due to bad weather. its average speed is reduced by 100km/hr and time increased by 30 minutes. find the original duration of the flight.

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## In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hour and time increased by 30 minutes. Find the original duration of flight.

Click here👆to get an answer to your question ✍️ In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hour and time increased by 30 minutes. Find the original duration of flight.

Question

## In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hour and time increased by 30 minutes. Find the original duration of flight.

**A**3

2 1 hours

**B**5

2 1 hours

**C**4

2 1 hours

**D**2

2 1 hours Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Let the original speed =x km/hr∴ Normal time of flight =

x 2800

hours ,New speed =(x−100)km/hr

∴ Time of flight, when speed is reduced =

x−100 2800 hours

According to the given condition,

(x−100) 2800 − x 2800 = 60 30 2 1 = x(x−100) 2800x−2800(x−100) ⇒x 2 −100x−560000=0 ⇒x 2 −800x+700x−560000=0

⇒x(x−800)+700(x−800)=0

⇒(x−800)(x+700)=0 ⇒x−800=0 x+700=0 ⇒x=800,−700

Neglecting the -ve value.

Original speed of the are craft = 800 km/hr

Original duration of flight =

800 2800 =3 2 1 hours

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## In a flight of 2800 km, an aircraft was slowed down due today weather. It's average speed for the trip was reduced by 100 km / hour and the time increased by 30 minutes. Find the original duration of flight.

In a flight of 2800 km, an aircraft was slowed down due today weather. It's average speed for the trip was reduced by 100 km / hour and the time increased by 30 minutes. Find the original duration of flight.

Byju's Answer Standard VIII Mathematics

Relation for Inverse Proportion

In a flight o... Question In a flight of 2800 k m ,

an aircraft was slowed down due to today's weather. It's average speed for the trip was reduced by

100 k m /

hour and the time increased by

30

minutes. Find the original duration of the flight.

Open in App Solution

Let the speed of aircraft be

x k m / h Distance travelled = 2800 k m Time taken = Distance Speed = 2800 x hours

Given that when the speed is reduced by

100 k m / h , New speed = ( x – 100 ) k m / h

, time is increased by

30 minutes That is, 30 minutes = 30 60 hour = 1 2 hour

Time taken after the speed was reduced

= [ 2800 ( x – 100 ) ] hour ∴ [ 2800 x – 100 ] = 2800 x + 1 2 ⇒ [ 2800 x – 100 ] − 2800 x = 1 2 ⇒ 2800 [ x − ( x − 100 ) x ( x − 100 ) ] = 1 2 ⇒ x 2 − 100 x − 560000 = 0 ⇒ x 2 − 800 x + 700 x − 560000 = 0 ⇒ x ( x − 800 ) + 700 ( x − 800 ) = 0 ⇒ ( x + 700 ) ( x − 800 ) = 0 ⇒ x = − 700 or, 800

Since speed cannot be negative,

x = 800.

Thus original duration of the flight

= 2800 800 = 7 2 hours = 3 hours 30 minutes Suggest Corrections 24

SIMILAR QUESTIONS

**Q.**In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.

**Q.**In a flight of

6000 k m

an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by

400 k m / h o u r

and time increased by

30

minutes. Find the original duration of flight.

**Q.**

In a flight of 2800km an aircraft was slowed down due to bar weather. If average speed is reduced by 100km/hr and time increase by 30min find the original duration of the flight.

**Q.**In a flight of

600 k m

, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by

200

km/hr and the time of flight increased by

30

minutes. The duration of the flight is:

**Q.**In a fight of

600 k m

, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by

200

km/hr and the time of flight increased by

30

minutes. Find the duration of flight.

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Standard VIII Mathematics

## In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.

In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.

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In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and time increased by 30 minutes. Find the original duration of the flight.

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### SOLUTION

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

If the speed of the plane is reduced by 100 km/hr, then

Reduced speed of the plane = (x − 100) km/hr

Time taken by the plane to reach its destination at original speed,

t1=2800xhr

Time taken by the plane to reach its destination at reduced speed,

t1=2800x-100hr Given,

Time taken by the plane to reach its destination at reduced speed − Time taken by the

plane to reach its destination at original speed = 30 minutes

t2-t1=12hr ⇒2800x-100-2800x=12

⇒2800x-2800(x-100)x(x-100)=12

⇒2800×x100×2=x2-100x

⇒x2-100x-560000=0

⇒x2-800x+700x-560000=0

⇒x(x-800)+700(x-800)=0

⇒(x-800)(x+700)=0 ⇒x-800=0 Or x+700=0 ⇒x=800 or x=-700 ∴x=800 ∴

[Speed cannot be negative]

Original speed of flight = 800 km/hr

∴ Original duration of flight,

t1=2800800=72=312Hrs

Thus, the original duration of the flight is 3 hours 30 minutes.

Concept: Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated

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