Respuesta :
Answer:
The original duration of the flight is of 5 hours.
Step-by-step explanation:
Given:
Total distance covered by the flight = [tex]3000[/tex] km
Let the speed of the flight in normal condition be [tex]x[/tex] km/hr
And the average speed in bad weather = ([tex]x-100[/tex]) km/hr
Time taken increases when the speed of the flight decreases.
Time taken in normal condition, [tex]t_1[/tex] = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{3000}{x}[/tex] hr
Time taken in bad weather, [tex]t_2=\frac{3000}{x-100} +1[/tex] hr
Here we can observe the difference of time = [tex]1[/tex] hr
So,
⇒ [tex]t_2-t_1 =1[/tex]
⇒ [tex]\frac{3000}{(x-100)}-\frac{3000}{(x)} =1[/tex]
⇒ [tex]\frac{3000(x)-3000(x-100)}{(x)(x-100)} =1[/tex]
⇒ [tex]3000(x)-3000(x-100)=(x)(x-100)[/tex]
⇒ [tex]3000x-3000x+300,000 =x^2-100x[/tex]
⇒ [tex]x^2-100x-30,000=0[/tex]
⇒ [tex]x^2-600x+500x-300,000=0[/tex] using middle term splitting method.
⇒ [tex]x(x-600)+500(x-600)=0[/tex]
⇒ [tex](x+500)(x-600)=0[/tex]
⇒ [tex]x=600 ,-500[/tex]
Note: We can also use quadratic formula directly to find 'x' values.
Discarding the negative value as speed can't be negative.
Speed of the flight in normal condition = [tex]600[/tex] km\hr
Speed of the flight in bad weather = [tex]500[/tex] km\hr
Original duration of the flight = Ratio of distance and speed in normal condition.
⇒ Original duration = [tex]\frac{3000}{600}= 5[/tex] hr
But due to bad weather the duration of the flight will be an hour more that is [tex]6[/tex] hrs.
The original duration of the flight is 5 hours.
