Question

In a flight of 600km ,an aircraft was slow down due to bad weather .its average speed for the trip was reduced by 200km/hr and the time increased by 30 minute..find the duration of the flight?

Answer 1

so distance = 600 km
let the speed be x km/hr
and
 time be t hr  = 600/x

now when it was delayed so speed now is (x - 200) km/hr
and time = t₁ = 600/(x- 200)
so according to the question

 t₁ - t = 1/2

600 (1/(x-200) - 1/x) = 1/2
⇒1200 (x - x + 200) = 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

so x = - 400 or 600 so speed can't be negative

so x = 600 km/hr 

So the time = 600/600 = 1 hr ANSWER

Answer 2

Answer:

The duration of the flight is 1hr.

Step-by-step explanation:

Using middle term splitting,

Let the original speed of the aircraft be $\mathrm{x} \mathrm{km} / \mathrm{hr}$

New speed $=(x-200) \mathrm{km} / \mathrm{hr}$

Duration of the flight at original speed $=\frac{600}{x} \mathrm{hr}$

Duration of the flight at the new speed $=\frac{600}{x-200} \mathrm{hr}$

According to the given question,

$\frac{600}{x-200}-\frac{600}{x}=\frac{1}{2}$

$\frac{600 x-600(x-200)}{x(x-200)}=\frac{1}{2}$

$\frac{120000}{x(x-200)}=\frac{1}{2}$

$240000=x(x-200)$

$240000=x^{2}-200 x$

$x^{2}-200-240000=0$

$x^{2}-600 x+400 x-240000=0$

$x(x-600)+400(x-600)=0$

$(x+400)(x-600)=0$

$x=-400$

or  $x=600$.

X cannot be negative. therefore, the original speed of the aircraft existed 600 km/hr.

Thus, the duration of the flight $\frac{600}{x} \mathrm{hr}=1 \mathrm{hr} .$

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