Aptitude - Time and Distance - Discussion

Let the speed be 'S' kmph and time 't' hr.

So S = 600/t --- (1).

And since speed got reduced by 200 and time increased but 30 min.

So (s - 200) = 600/ (t + 30/60) --- (2).

Solving 1 and 2 equation we will get:

2t^2 + t-3 = 0 --- (3).

By equation 3 we will get:

t = -3/2 or t = 1/2.

Since time can't be negative. So t = 1/2.

Putting this value in equation 1.

We will get t = 1/2.

But we have to find how much time it will take after it got slowed.

So total time = 1/2 + 30/60 = 1/2 * 2 = 1 hours;

How can we add. Minutes to the hours like 200 hours and 30 minutes.

Simple friends, we solve by using S = D/T.
S - speed.
D - distance.
T - Time.
S = 420/t --> (1).
S + 10 = 420/(t-1) --> (2).
From(2) St- S+ 10t-10 = 420 --> (3)

Let equate (1) and (3), from this we can find speed.
St = ST - S + 10t - 10.
(OR) T = S+10/10.

Now S = D/T.
Substitute the values S = 420/S + 10/10.
S = (420*10)/(S+10).
S = -70 and 60. Neglect the negative S=60.

@Rahim Shaikh.

There is a small mistake in your answer.

Tt will be:
(x - 600) (x + 400) = 0.
x2 - 200x - 240000 = 0.
Not x+200. Check this once.

How you got 1200/2x+1? Please explain it.

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.