Aptitude - Time and Distance - Discussion

Dear all.

I think ,duration of the flight is 1.5 hour.

With the calculations, normal speed = 600 km/hr.
So reduced speed = 600 - 200 = 400 km/hr.
To cover the journey of 600 km @ 400 km/hr time taken = 600/400 = 1.5 hour.

600/x - 600/x + 1/2 = 200,

First solve the denominaor of 600/x + 1/2,

600/x - 600 * 2/2(x) + 1 = 200,

600/x - 1200/2x + 1 = 200,

Take LCM, 600(2x + 1) - 1200(x)/x (2x + 1) = 200,

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

As we can see 1200x substract from 1200x,

So the new equation is 600/x (2x + 1) = 200,

Or we can say 600/200 = x(2x + 1),

Now 3 = x(2x + 1),

2x^2 + x - 3 = 0,

2x^2 - 2x + 3x - 3 = 0.

2x (x - 1) + 3 (x- 1) = 0.

(2x + 3) (x - 1) = 0.

x = 3/2 or x = 1.

Let the duration of the flight be x hours.

Then, 600 - 600= 200.

x x + (1/2).
600 - 1200 = 200.
x 2x + 1.
x (2x + 1) = 3.
2x^2 + x - 3 = 0.
(2x + 3) (x - 1) = 0.

Then, x = 1 hr.

Let, x is original speed.

(600/x - 200) - (600/x) = 30/60,
Solving this equation, we get x = 600.
Duration of flight = 600/600 = 1 hr.

One hour answer is logically wrong. If we assume that original speed was 800 km/hr, then, 600/800 = 45mints will be the time taken at original speed.

And after reduction of 200 km/hr new speed will be 600 km/hr, then time would reduce by 15 mints, not 30 mints.

30 mints can only be possible if original speed was 600km/hr which is reduced to 400km/hr. then 600/400 = 1.50, which is 1 hour and 30 mins.

And y = original time taken.
So 600/x = y--------(1).

Now we know if speed reduces 30 minutes more will be taken.
i.e 30/60 hours.

So,
600/x-200 = y+30/60, here 30/60 means 30 minutes.

Now put the value of y as shown in (1),
So equation will be,
600/x-200 = 600/x - 30/60.

You will get,
x2-200x-240000 = 0 here x2 means x square.
(x-600)(x+200) = 0.
X = 600.

That's why
Time = 600/600.
=1 hours.

So Total Time need for Flight =(1hour + 30 min) = 1.5 hours. ANSWER. :-)

@Babita.

Why are we taking 600-6000=200?

Can anyone give me the explanation?

distance = 600km, speed x kmph.

t = 600/x-----Actual time taken by journey.

t + 30 = 600/x - 200------> this due to reduce speed, x-200, 200kmph speed reduce from actual speed.
t = (600/x-200) - 30.

600/x = (600/x-200)-30/60------30min convert to hrs
600/x = (600/x - 200)-1/2,
600/x - 200 - 600/x = 1/2,
[600x - (x - 200)600]/x(x - 200) = 1/2,
x^2-200x - 240000 = 0,
x^2-600x + 400x - 240000 = 0,
x(x-600) + 400(x-600) = 0,
x-600 = 0,&x + 400 = 0 +ve values only consider.

x = 600kmph.
Actual journey time = 600/600 = 1hr.

I have one doubt, due to bad weather the time increased by 30 min then we should add 30 min in x ie (x+30/60) or not?

Please help me.

Assume the normal time of flight was X.
Due to bad weather it was X+30 convert it into hours it would be X+ 1/2.
Normal speed of flight be S.
Due to bad weather, it was S-200.

First equation would be S = 600/X,
Second one would be S-200= 600/X+ 1/2.
Solve them equate Find the value of X by Equating in terms of X to each other
600/X=(1200/ 2X+1 )+ 200.