Question

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

Answer 1

Given that distance = 600 km

Let the normal speed of the aircraft be x km/hr and time taken be T.

Case I:

Speed = `"Distance"/"Time"`

`x = 600/T`

`T = 600/x`   ...(i)

Case II:

T = 30 minutes

`T = 30/60 hr`

`T = 1/2 hr`

Speed = `"Distance"/"Time"`

`x - 200 = 600/(T + 1/2)`

`T + 1/2 = 600/((x - 200))`   ...(ii)

From equation (i), insert the value of T in equation (ii),

`T + 1/2 = 600/(x - 200)`

`600/x + 1/2 = 600/(x - 200)`

∴ `600/(x - 200) - 600/x = 1/2`

`600 [1/(x - 200) - 1/x] = 1/2`

`600 [(x - (x - 200))/(x(x - 200))] = 1/2`

`600 [(x//-x - 200))/(x^2 - 200x)] = 1/2`

`600 [(200)/(x^2 - 200x)] = 1/2`

`120000/(x^2 - 200x) = 1/2`

2(120000) = x² – 200x

240000 = x² – 200x

x² – 200x – 240000 = 0

x² – 600x + 400x – 240000 = 0

x(x – 600) + 400(x – 600) = 0

(x – 600)(x + 400) = 0

x – 600 = 0

x = 600

x + 400 = 0

x = –400

(Not possible as speed cannot be negative)

∴ x = 600 km/hr

Now, from equation (i)

`T = 600/x`

= `(600  km)/(600  km//hr)`

= 1 hr

∴ Scheduled duration of the flight is 1 hour.