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.
A32 1 hours
B52 1 hours
C42 1 hours
D22 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 of6000 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
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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 of600 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 of600 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.
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