Question

in a fight of 600 Km; an aircraft was slowed down due to bad weather. its average speed for the trip was reduced to 200 Km/hr and the time increased by 30 minutes. find the duration of the flight.(hint quadratic equation)

Answer 1

Answer:

The total duration of flight is 0.385 seconds .

Step-by-step explanation:

The Total distance of flight = d = 600 km

Let the time taken to cover 600 km = t hours

And The speed of the flight = s km/hr

∵ Distance = speed × time

So, s × t = 600                ...........1

Now, The speed of the trip reduced by 200 km/h

So, The reduced speed = ( s - 200 ) km/h

And , The time increase by 30 minutes

So, The increase time = ( t + $\dfrac{30}{60}$ ) hours

I.e The increase time = (t + 0.5 )hours

Or,  (s - 200) × (t + 0.5 ) = 600

Or, s × t + 0.5 s - 200 t - 100 = 600        ........2

Now, Put the value of s from eq 1 ino eq 2

So, 600 + 0.5 × $\dfrac{600}{t}$ - 200 t - 100 = 600

Or, $\dfrac{300}{t}$ - 200 t = 600 + 100

Or, $\dfrac{300}{t}$ - 200 t = 700

Or, 300 - 200 t² = 700 t

Or, 2 t² + 7 t - 3 = 0

Now, solving the quadratic equation in the form of a x² + b x + c = 0

t = $\dfrac{- b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

i.e t =  $\dfrac{- 7\pm \sqrt{7^{2}-4\times 2\times (-3)}}{2\times 2}$

Or, t = $\dfrac{- 7\pm \sqrt{73}}{4}$

Or, t = $\dfrac{-7+8.54}{4}$ , $\dfrac{-7-8.54}{4}$

Or, t = 0.385 seconds

So, The duration of flight = t = 0.385 seconds

Hence,The total duration of flight is 0.385 seconds . Answer