Aptitude - Time and Distance - Discussion

I will suggest one more formula to solve this kind of problems when stoppage time has to be calculated.

Then, stoppage time = 1-Slower speed/Faster speed.

Hence in this case.

= 1-45/54.
= 1- 5/6.
= (6-5)/6.
= 1/6.

Which can be converted to = 1/6*60 = 10 min.

Suppose bus will take t hours to cover certain distance, if there are stoppages, as we know speed = d/t = = 45kmph.

Total distance covered by bus = speed*time = 45t....equation(1).

If bus did not stop at those stoppages, where stoppage time was s hours, then bus actually saved s hours to cover same distance.

It means that due to travel time of (t-s) hours, the speed was increased, as we know speed = d/(t-s) = 54kmph.

Total distance covered by bus = speed*time = 54kmph*(t-s) = 54t - 54s...equation(2).

From equation (1) and (2),

54t-54s = 45t.

=> 54t-45t = 54s.
=> 9t = 54s.
=> 9t/54 = s.
=> s = t/6.

If t = 1 hour = 60 minutes,

Then, s = 60/6 = 10 minutes.

How can you take if t=1 randomly?

There is a formula for this questions:

(V1-v2)/v1.

V1= Without stoppage velocity.

V2 = With stoppage.

Result is in hour. Multiply by 60 to get minutes.

For 60 min......54 kmph so.

For ? min.......45 kmph.

= 45*60/54 = 50 mins it means 10 mins less so it has stopped for 10 mins.

We are taking 9/54, because car is moving @ 54 not 45 km/hr. The question is on average speed which means total distance divided by total time.

Now, because car waits for some minutes at stops that is why average speed gets decreased. So, speed is same which is 54 km/hr, but including stoppages total time has increased. Therefore average speed comes down.

Formula:

If a body moves at an average speed of V1 km/hr to cover a distance of D km without stopping and moves at an average speed V2 km/hr to cover the same distance.

Then stoppage time/hour is: (V1-V2) /V1.

= (54-45)/54 = 10 mins.

Well said @Nitesh Nandwana.

It's simple and easy to solve.

Why we considered 54?

Let's do this way:
Let us consider a distance d km and the second vehicle takes x time more.

Then,
D = 54km/hr * 1hr as 54km/hr is without stoppage so it'll take.

Less time.
D = 45km/hr * (1 + x) including stoppage will take more time to.

To cover d km.

54 * 1 = 45 (1 + x).
54 - 45 = 45x.
9 = 45x.
The, x = 9/45 = 0.2hr.

=> 0.2hr = 0.2 * 60 min = 12 min.

Hi, I'm not getting this. Can anyone explain me clearly?