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 average speed of the flight......

Answer 1

Correct 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. The duration of the flight is?

To find: We have to find the average speed of flight.

Answer: The average speed of flight is 1 Hour.

Explanation:

Let the duration of flight be x hours.

∴ Reduced speed of flight = Original speed of flight - New speed of flight

Original speed = 600/x

New speed = 600/x+1/2

= 600/x - 600/x+1/2 = 200

= 600/x - 400/x = 200

= 1

Therefore, X = 1

Therefore, Duration of flight is 1 hour.

Explanation:

In the given question, The distance of flight is given as 600 km. The flight was slowed down due to bad weather. And hence, The average speed of flight was reduced by 200 km/hr. Also, The time of flight was increased by 30 minutes. We solved the problem by taking the variable X as hours. By putting the proper values, We find the value of x and we get 1. Hence, The duration of flight was 1 hour.

Answer 2

Correct 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.

AnswEr :

$\bf{\dag}\:\underline{\sf we \:have :}\\\\\bullet\:\:\sf Distance = 600 \:km\\\\\bullet\:\:\sf let\:Old\:Time= n \:hr\\\\\bullet\:\:\sf let\:New\:Time=\bigg(n+\dfrac{30}{60}\bigg)=\bigg(n+\dfrac{1}{2}\bigg)=\dfrac{(2n + 1)}{2}\:hr$

$\rule{150}{2}$

$\bigstar\:\large\boxed{\sf Speed =\dfrac{Distance}{Time}}$

$\rule{200}{1}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\texttt{Old Speed - New Speed = 200 km/hr}\\\\\\:\implies\tt\dfrac{600}{n} -\dfrac{600}{ \frac{2n + 1}{2}} = 200\\\\\\:\implies\tt600\bigg(\dfrac{1}{n} - \dfrac{1}{ \frac{2n + 1}{2}} \bigg)=200\\\\\\:\implies\tt\dfrac{1}{n} - \dfrac{2}{2n + 1} =\dfrac{200}{600}\\\\\\:\implies\tt \dfrac{2n + 1 - 2n}{n(2n + 1)} =\dfrac{1}{3}\\\\\\:\implies\tt \dfrac{1}{2{n}^{2} + n} = \dfrac{1}{3}\\\\\\:\implies\tt3 = 2{n}^{2} + n\\\\\\:\implies\tt2{n}^{2} + n - 3 = 0\\\\\\:\implies\tt2{n}^{2} + (3 - 2)n - 3 = 0\\\\\\:\implies\tt2 {n}^{2} + 3n - 2n - 3 = 0\\\\\\:\implies\tt n(2n + 3) - 1(2n + 3) = 0\\\\\\:\implies\tt(n - 1)(2n + 3) = 0\\\\\\:\implies\tt \green{n = 1 \:hr} \quad or \quad \red{n =\dfrac{ - 3}{2} \:hr}$

⠀

$\therefore\:\underline{\textsf{Ignoring -ve, Duration of Flight is \textbf{1 hr}}}.$