Aptitude - Time and Distance - Discussion

I solve this problem like this

First, I check the facts given:
Distance = 600km.
Original speed = we don't know,
New speed = we don't know,
The Relation between new and original speed = new speed is 200km/h slower to original speed so the diff in speed is 200km/h.
Original time = we don't know,
New time = we don't know,
Relation between new and original Time = new time is 30minutes more than original time so the diff in time is an hour.

Now, I need two separate numbers with the diff of 200 and should be able to divide 600 with a diff of .5 (means) and the numbers are 600 and 400.

600/600 = 1 (original speed 600km/h and it takes 1 hour to reach).
600/400 = 1.5 (new speed 400km/h and it takes 1 hour 30 min to reach).

Suppose,
Duration = x hour.
600-200 = 400,
ATq,
x/400 - x/600 = 1/2,
2x = 1200,
x = 600,
So,
duration = 600/600 = 1 hour.

In question avg speed given:

The avg speed= total distance/total time elapsed
So according to question the equation becomes:
1200/2t - 200 =1200/(2t+1/2).

After solving,
4t^2+t-3=0,
(4t+3)(t-1)=0,
so t=1;(taking positive value).

Another simple way of doing this is solve by;

600/(x-200)- 600/(x) = 1/2.
we get x= 600km/hr.

Time=distance/speed = 600/600 = 1hr.

Yesh, I understood till,

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

Please, can anybody simplify this, only let me know, please.

@Patreppa.

((2x+1)600-1200x)/x(2x+1)=200
(1200x+600-1200X)=200*x(2x+1)
600=200(2x^2+x)
600=400x^2+200x
400x^2+200x-600=0

Divide by 200 then(just for simplification).

2x^2 + x - 3 = 0.

Distance=600km
Speed=200km
Time=x+30mins

So we have to the time duration,
Time = Distance/speed.
x+30=600/200,
x+30=3,
x=3-30,
x=27mins(neglect the negative),
x=27+30min,
x=57 mins(Almost 1hr),

Ans x=1hr.

Let the time be x.

Total speed(Dis/time) - actual speed due to weather(dis/time) = reduced speed.

600/x - 600/ x+(1/2) = 200.
Here actual speed is less because of weather condition, which means it has taken MORE TIME which is 1/2 hour or 30 min.

Solve answer you get an answer as 1 hr.

Thanks @Kiran.

Change in in speed i.e speed reduced by 200 kmph then change in time is 30 mnts.
If speed reduce to zero i.e by 600kmph. Time taken will be 90 mnts.

As mentioned in the question, Flight took 30 months more.
To find the original time of flight, 90 -30 = 60 months, i.e 1 hour.