Aptitude - Time and Distance - Discussion

2x^2 - 2x + 3x - 3 = 0. How we get it? Explain.

Does anybody think the 1/2 should be added to make the answer to 1.5hr?

Why should we take the diff between the velocity's as reduced speed?

Please briefly explain any one.

600/x = 1200/2x+1+200.
600/x = 1200+(2x+1)(200)/2x+1 (for whole 2x+1).
600/x = 1200+400x+200/2x+1 (for whole 2x+1).
2x+1(600) = x(1200+400x+200).
1200x+600 = 1200x+400x^2+200x (cancel 1200x on bboth sides).
So 400x^2+200x-600.

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.

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.

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.

@Babita.

Why are we taking 600-6000=200?

Can anyone give me the explanation?

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. :-)

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.