Aptitude - Time and Distance - Discussion

54 km in 60 minutes.

9km in x.
Cross multiply.
60 * 9 =540/54.
Is equal to 10 minutes.
So, 9km is taking 10 minutes to stop.

The LCM approach here makes our work easy. This can even be applied in problems on pipes and cisterns, work and time, etc.

So, first, take the LCM of 54 and 45 to be the distance covered i.e. 270 km.

The time taken without stoppage is 270/54 = 5 hrs. The time taken with stoppage is 270/45 = 6 hrs. This implies that out of 6 hrs, 1 hour accounts for the stoppage because 6-5 = 1.
Next, apply the unitary method.

6hrs ---------- 1 hr of stoppage.
1 hr ----------- (1/6)*60 = 10 mins stoppage.

Analogously, in case of pipes and cisterns, the lcm of the time taken by the pipes to fill/empty can be taken as the total capacity of the cistern.

Without stops, Bus travels - 54 Km in 1 hr.
With stops, the bus travels- 45 Km in 1 hr.

So the extra distance the bus could have travelled if there weren't any stops= 54-45=9 Km.
So the time is taken for travelling that 9 Km is the same as the time taken for the stops,
V = d/t.
54 = 9/t.
t = 9/54 hrs=(9/54)*60=10 min.

Here, the confusion is how come 45/54?

However, the main thing to be noted is that the bus travels at 54kmph in both cases. However, due to stopping for some time, the average speed becomes 45 in case 2. Whereas in the first case, the 54kmph average is the same as its speed because it never stops.

So considering one hour of time, the bus itself covers 45km instead of 54km. We have a difference of nine kilometers in the distance traveled. But we cannot used the average speed of 45 since it travelled at 54 irrespective of the case.
So 9/54 becomes 1/6 hours or 10 minutes.

Good explanation, thanks @Jaya.

Stoppage time = difference of speed/maximum speed.
= 54-45/54 * 60min,
= 9/54 * 60min,
= 1/6 * 60min.
= 10min.

I didn't understand, I'm confused about this stoppages can anyone explain in detail?

You were excellent! Thanks, @Jaya and @Kushal.

2 speeds difference is 9 km,
So we should calculate the time taken to cover 9 km.
So, 9/54*60 =?
Then the answer is 10 minutes.

Can anyone tell me the easy method.