Aptitude - Time and Distance - Discussion

I have a quest actually the time is x+1/2 hours after delay that's the whole duration of flight but its taken as only x now its actually x+1/2 = 1 and half hour.

I have a doubt in the question its average speed for the trip was reduced by 200 km/hr is given but trip means both up and down so that its 1200 kms but in the answer only 600 km is taken.

In this question I have a doubt its average speed for the trip was reduced by 200 km/hr i.e., trip means both upside and downside distance. Such that the distance is 1200 km (600 km for upside and 600 km for downside).

The distance is same in both cases and let time in case 1 be t.

Then 600 t = 400 (t+30/60).

Thus t = 1 hr.

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.

How will 2x+1 will come it it 600/(x+1/2) = 1200/x+1?

@Ben You are right.

I am just copying a comment listed above.

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 why 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.

In the above equation we solved x to be 600 where x is the average speed when there isn't any bad weather. But there was bad weather and the flight slowed down to 400 kmph (600kmph-200kmph).

So the time taken for the actual flight due to slow down is 600km/(600kmph-200kmph).

i.e 1 and 1/2 hours.

I don't why but this is the second time they have used the difficult method. They use the basic principle to assume the variable to find as x i.e. time of flight as x. I don't follow this always.

Let's do the opposite way. Let us assume the original (or misleadingly called average) speed as x. Now if speed is decreased.

Then the time is increased by 30 mins i.e. 30/60 hrs (since we are using kmph so time has to be in hrs).

Now using common sense logic. If less speed then more time to travel the same distance.

So here the time difference for the two speeds is 30 mins or 30/60 hrs.

i.e (Time with less speed) - (Time with faster speed) = 30/60 hrs.

Now Time = Distance/Speed.

(600/(x-200))-600/x = 30/60.

Solve this equation to get x = 600 kmph.

600 km/600 kmph = 1 hr simple as that.

Just seems lengthy because I explained the logic. But its not always good to assume the unknown as x. This method seems easier to me.

Any one solve this simple and shortly? How this x+1/2 came? I'm not getting.

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.