Aptitude - Time and Distance - Discussion

@All.

Consider the distance is only 54 kms. At 54 kmph it will take only 1 hr.
But since due to stoppages it takes 10 minutes extra (the time of stoppages).
So, shouldn't we get 45 kmph if we divide 54 km the distance by 1 hr 10 minutes (70 minutes)? We don't get that, of course. The bus runs at 54 and with the stoppage, rit reaches 45 km. 9 km is remaining. The average speed with stoppages was 45kmph. the remaining distance of 9 km has to be completed by that average speed as there are no more stoppages to get the correct time taken by the bus and not by 54kmph.

So, it will work out to be 12 minutes, not 10 minutes.

Its very simple,

Firstly,
54 - 45 =9 due to stoppages,it covers 9km less.
Time taken to cover 9km = (9/54 x 60) =10mins. And in "1 min there are 60 seconds".

See, the problem is simple, but we just require a way of understanding it.

Speed is 54kmph. That is clear. Now it says that due to the inclusion of 'stoppage' it is 45kmph. We need to understand that this just means that it appears to be 45kmph due to stoppage, which further means that where it had the potential of covering 54km in 1hr, it is now covering 45km in 1hr (but the speed is going to remain, just that the bus stops, hence time is consumed there, otherwise the speed is same only).

So (actual speed)*(1hr - time wasted due to stopping) = 45

Actual speed = 54kmph, and the time wasted has to be found out.

1hr - wasted time shows the effective moving time, due to which, while travelling at 54kmph, the bus covered a 45km distance only.

I hope it clears the doubt.

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = 9 x 60 min = 10 min.

@All.

Here is my solution;

For me, in 1 hour the bus runs 54 km by the speed of 54km/h excluding stops.
But because of stop time, it runs by a speed 45km/h.
That means 54 km/ times = 45 ( km/h).
So the total times needed is 54/45 = 6/5 h,
And stop time is 6/5 -1 = 1/5h = 12 minutes.

54kmh means it travels 54 kms in one hour when the train runs continuously in that hour. However including stoppages the train travels only 45 km in one hour. Thus in one hour train travels 9 km less due to stoppages.

Thus the time the train stops in an hour is the time it would have used to travel 9kms with the speed of 54kms, which when converted to minutes is equal to 10.

Non stoppages speed= 54kmph,
with stoppages speed= 45kmph.

Reduce speed due to stoppages = 54-45 = 9 kmph.
we need to find the time taken by bus at a stop in each hour i.e t
t = s/v,
t = 9/54 ph ( we take 54 because we are talking about non-stoppages).
= 1/6 *60 min.
=10 min.

@All.

As per my knowledge, to solve this question, we can use the concept of average speed.

Let's denote the time the bus stops per hour as (T) minutes.

The speed without stoppages is 54 kmph, and the speed with stoppages is 45 kmph.

The time taken to cover the same distance without stoppages = 60 minutes.
The time taken to cover the same distance with stoppages = 60 + (T) minutes.

Using the formula for average speed: Average Speed = Total distance/Total time.

We can set up the equations:
54 = Total distance/60
45 = Total distance/(60 + (T)).
Now, solve for (T) minutes to find out how many minutes the bus stops per hour.

Thanks for explaining @Anoo.

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = 9 x 60 min = 54.