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

The total duration of flight is 0.385 seconds .

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 +
`(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 ×
`(600)/(t)` - 200 t - 100 = 600

Or,
`(300)/(t)` - 200 t = 600 + 100

Or,
`(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 =
`\frac{- b\pm \sqrt{b^(2)-4* a* c}}{2* a}`

i.e t =
`\frac{- 7\pm \sqrt{7^(2)-4* 2* (-3)}}{2* 2}`

Or, t =
`(- 7\pm √(73))/(4)`

Or, t =
`(-7+8.54)/(4)` ,
`(-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