# in a flight of 600 km, an aircraft was slowed down due to bad weather. the average speed of 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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## [Solved] In a flight of 600 km an aircraft was slowed down due to bad

Given: Total Distance = 600 km. average speed was reduced = 200 km/hr the time of flight increased = 30 minutes Formula Used: ∵ Average Speed = Tot

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## In a flight of 600 km an aircraft was slowed down due to bad weather. Its average speed was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is;

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## Detailed Solution

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**Given:**

Total Distance = 600 km.

average speed was reduced = 200 km/hr

the time of flight increased = 30 minutes

**Formula Used:**

∵ Average Speed = Total Distance / Time

**Calculations:**

Let, the original duration of flight be t hrs.

So, original average speed = 600/t

Due to bad weather speed of trip is reduced by 200 km/hr and time of flight is increased by 30 minutes i.e. 0.5 hr.

∴ Reduced average speed = (600/t) – 200

And New duration of flight = (t + 0.5) hrs

So, the new average speed = 600/(t + 0.5)

Equating,

⇒600t−200=600t+0.5⇒3t−1=3t+0.5⇒3−tt=3t+0.5

⇒ t2 + 0.5t – 1.5 = 0

⇒ 2t2 + t – 3 = 0

⇒ 2t2 – 2t + 3t – 3 = 0

⇒ (t – 1)(2t + 3) = 0

⇒ (t – 1) = 0 ∴ t = 1 hr

**∴ The duration of the flight is 1 hr.**

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## In a flight of 600km, an aircraft was slowed down due to bad weather

Question 32 (Choice 2) In a flight of 600km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30 min. Find the scheduled duration of the flight.Let the speed of aircarft be x km/hr

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## Question 32 (Choice 2) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at March 16, 2023 by Teachoo

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

This question is Similar to Ex 4.3 - Chapter 4 Class 10

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### Transcript

Question 32 (Choice 2) In a flight of 600km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30 min. Find the scheduled duration of the flight.Let the speed of aircarft be x km/hr Normal speed Distance = 600 km Speed = x km/hr Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒 x = 600/𝑇𝑖𝑚𝑒 Time = 𝟔𝟎𝟎/𝒙 Speed reduced by 200 km/h Distance = 600 km Speed = (x − 200) km/hr Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒 x − 200 = 𝟔𝟎𝟎/𝑻𝒊𝒎𝒆 Time = 𝟔𝟎𝟎/(𝒙 − 𝟐𝟎𝟎) Given that Its average speed for the trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30 min Time when speed reduced − Time normal = 30 minutes Time when speed reduced − Time normal = 𝟏/𝟐 hour 𝟔𝟎𝟎/(𝒙 − 𝟐𝟎𝟎)−𝟔𝟎𝟎/𝒙=𝟏/𝟐 (600𝑥 − 600(𝑥 − 200))/(𝑥(𝑥 − 200))=1/2 (600𝑥 − 600𝑥 + 120000)/(𝑥^2 − 200𝑥)=1/2 120000/(𝑥^2 − 200𝑥)=1/2 2 × 120000 = x2 − 200x 240000 = x2 − 200x x2 – 200x − 240000 = 0 x2 − 200x – 240000 = 0 Comparing with ax2 + bx + c = 0 a = 1, b = −200, c = −240000 Roots of the equation are given by x = (− 𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎 Putting values x = (−(−200) ± √(〖(−200)〗^2 − 4 × 1 × (−240000) ))/(2 × 1) x = (200 ± √(40000 + 4 × 240000))/2 x = (200 ± √(40000 + 960000))/2 x = (200 ± √1000000)/2 x = (200 ± √(〖10〗^6 ))/2 x = (𝟐𝟎𝟎 ± 𝟏𝟎𝟎𝟎)/𝟐 Hence x = 600, x = –400 are the roots of the equation x = (200 + 1000)/2 x = 1200/2 x = 600 x = (200 − 1000)/2 x = (−800)/2 x = –400We know that Speed of flight = x So, x cannot be negative ∴ x = 600 is the solution So, Speed of flight = x = 600 km/hr But, we need to find the scheduled duration of the flight. Scheduled Duration = Time = 𝟔𝟎𝟎/𝒙 = 600/600 = 1 hour

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## In a flight of 600 km, 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. What is the duration of the flight? Maths Q&A

In a flight of 600 km, 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. What is the duration of the flight? Get the answer to this question and access a vast question bank that is tailored for students.

Byju's Answer Standard VIII Physics Speed In a flight o... Question In a flight of 600 km

, 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. What is the duration of the flight?

Open in App Solution

**Step 1: Given**

Total distance, d=600 km

Average speed was reduced by

200 km/hr

Time of the flight increased by

30 minutes

**Step 2: Find the new average speed of the flight**

Let t

be the original duration of the flight

The original average speed of the flight was

600t

Hence, the new average speed is

s=

Original speed - Reduced speed

=600t-200

**Step 3: Find the new duration of the flight**

Let the new duration be** **

t1 t1=

Original duration + Increased time

=t+0.5 hr

**Step 4: Find the new average speed**

The new average speed

=dt1 =600t+0.5

**Step 5: Equate the new average speeds**

600t-200=600t+0.5

Dividing by 200 on both the sides, we get

⇒ 3t-1=3t+0.5 ⇒t2+0.5t-1.5=0 ⇒ (t-1)(2t+3)=0 ⇒ t=1

**Therefore, the duration of the flight is**

1

**hour.**

Suggest Corrections 46

SIMILAR QUESTIONS

**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.

**Q.**

**In a flight of**

600 km

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

200 km/h

**and the time of flight was increased by**

30 min

**. Find the duration of flight.**

**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.

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