In a flight of 2800 km, an aircraft was slowed down due to bad weather

1.	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
Answer» Question : 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 To Find : The original duration of the flight GivEn Data : Average speed of the flight was reduced by 100 km/hr Time increased by 30 minutes Let us assume : The original speed of the flight be x Solution : Distance covered = 2800 km Now according to the formula to get time we see Time = Distance/Speed Time = 2800/x hr Given that the speed is decreased by 100 km/hr = x - 100 km Again, Time travel at reduced speed = Distance/Speed → 2800/(x - 100) Time taken = 30 mins → 1/2 hr So, $\sf \looparrowright \frac{2800}{x - 100} - \frac{2800}{x} = \frac{1}{2}$ $\sf \looparrowright \frac{2800x}{x(x - 100)} - \frac{2800(x - 100)}{x(x - 100)} = \frac{1}{2}$ $\sf \looparrowright \frac{2800}{ {x}^{2} - 100x} - \frac{2800x - 280000}{ {x}^{2} - 100x } = \frac{1}{2}$ $\sf \looparrowright \frac{2800x - 2800x + 280000}{ {x}^{2} - 100x } = \frac{1}{2}$ Now to cancel 2800x from 2800x $\sf \looparrowright\frac{ \cancel{2800} - \cancel{2800} + 280000}{ {x}^{2} - 100x} = \frac{1}{2}$ $\sf \looparrowright \frac{280000}{ {x}^{2} - 100 } = \frac{1}{2}$ By cross multiplying we get $\sf \looparrowright2 \times 280000 = {x}^{2} - 100$ $\sf \looparrowright560000 = {x}^{2} - 100$ We need to take 0 for factorisation $\sf \looparrowright {x}^{2} - 100x - 560000 = 0$ Now we have to split the middle term $\sf \looparrowright {x}^{2} - (800 - <klux>700</klux>)x - 560000 = 0$ $\sf \looparrowright {x}^{2} - 800x + 700x - 560000 = 0$ We have to take the common in them and then we can factorise $\sf \looparrowright x(x - 800) + 700(x - 800) = 0$ Taking (x - 800) as common we get $\sf \looparrowright(x - 800)(x + 700) = 0$ Now we can see that x - 800 = 0 x = 800 x + 700 = 0 x = - 700 As we know that speed cannot be NEGATIVE so the original speed is 800 Hence, the original speed of the flight is 800 km/h Now, the time taken = 2800/x Putting x's value we get Time taken = 2800/800 = 7/2 hrs → 3 hr 30 mins ∴ The time taken is 3 hr 30 mins Regards # BeBrainly

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

Answer»

Question :

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

To Find :

The original duration of the flight

GivEn Data :