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;

Distance = 600 km.
Average speed = 200 km.

If time taken is x min therefore the increased value of time = (x+30)min = (x+30)/60 hrs.

So by applying the formula of speed i.e. S=D/T, we get,

600 km=200 kmph/((x+30)/60)hrs.

600km = 200kmph*60/(x+30).

(600x+ 1800)km = 1200kmph.

Now by leaving the units as they are hrs for time , we get,

600x= 1200-1800.
600x = -600.

x = -600/600.
x = -1.

Since time can never be negative, Therefore by leaving the negative sign we get, x=1 hr.

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.

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. :-)

Guys I don't understand this problem. Surely if you were to do the original trip at an average speed of 600 km/hr then you would do it in 1 hr, yes?

Then you reduced your average speed by 200 km/hr to 400 km/hr which would mean 600 km would take 1 hr 30 min at the new average speed, ergo increasing your time by 30 min.

So the trip would then take an hour and a half not an hour, so what am I missing? Or is the question asking for the original time of the trip.

Another method:
let x = original speed.

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.

Hope you guys understand

Its simple yeah.

Why because just try think about question.
Any question read at least 2 times.

Ans:

Speed is reduced by 200km per hour.(not reduced to).
So delay extra 30 minutes i.e. in hours 30/60 = 1/2 = 0.5;.
As we know s=d/t; d=600km; without delay time req to reach destination t=T.

So finally,

(600/t) = speed without any delay.
(600/T+0.5) = speed with delay.

From question,
200 = (600/t) - 600/T+0.5).

Then you will get the answer.

@ISHAN the speed of the car is 60km/hr.

1)Let the speed be x km/hr.

2)Given distance covers =420km we know time t= distance/speed.

3)So let t= 420/x.

4)Given if speed is 10km/hr more so time (t-1)= 420/(x+10).

We have considered t=t-1 above because they have mentioned 1hr less so 420/x - 420/(x+10)=(t-t-1) i.e total distance/totalspeed = time

5)By solving we get x^2+10x-4200=0 we get x=60 &-70 ignore -70... 60 is answer.

Let, The speed of flight is:xkm/hr.

The total distance travelled by flight is = 600km
The speed is reduced to = x - 200km/hr,
Time was taken with speed x = 600/x.
Similarly,

Time taken by flight with reduced speed = 600/(x-200)
By Given Condition,
(600/x) + 1/2 = 600/(x-200)
1200 + x/2x = 600/(x-200)
(x-200) * (1200+x) = 1200x
So, x^2 - 200x - 240000 = 0,
(x+400) * (x - 600) = 0,
So x = 600.
Time taken is = 600/600 = 1hr.

Let the time be x
600 / x = speed
1/2 hr = 30 mins
therefore,
600/x - 600 /x-1/2 = 200 [since speed = distance time^-1]
600/x - 1200/2x - 1 = 200
600(2x-1) - 1200(x)/ x(2x-1) = 200
2x^2 - x(200)= 600(2x-1) - 1200(x)
2x^2 - x = 3(2x -1 )- 6(x)
2x^2 - x = 6x - 3 - 6x
2x^2 - x = 3
2x^2 - x -3 = 0
(2x-3)(x-1) = 0
x = 1
or
x = 1.5
Since 1 hour is an alternative therefore the correct answer is 1 hour.