Aptitude - Time and Distance - Discussion

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.

@Naren.

Because 54Kmph was the actual speed and 45Kmph was the speed after stoppage.

Speed of bus ->54 km/ hr(without stopping the bus)
Speed of bus ->45 km/ hr( with stopping the bus)
Excluding - including stoppages.

(54km/hr - 45 km/ hr = 9km)
So, the distance is 9 km,
We have to find out the time,
T = D/S.
T= 9/54.
T= 1/6 hr.
( 1 hr -> 60 min).
T= 1/6 *60min.
T= 10 min.

Consider the covers 54km & 45km in an hour without stoppage and with stoppage respectively. Since he covers 9 km less in stoppage.
His normal speed without stoppage is 54 km/h.
So, the time required to cover this distance is 9/54 hours i.e. 1/6 hour or 10 minutes.

So, he waited for 10 minutes in stoppage.

Speed of bus ->54 km/ hr(without stopping the bus)
Speed of bus ->45 km/ hr( with stopping the bus)
Excluding - including stoppages.
(54km/hr - 45 km/ hr = 9km)

So, the distance is 9 km,
We have to find out the time,
T = D/S.
T = 9/54.
T = 1/6 hr.
( 1 hr -> 60 min).
T = 1/6 *60min.
T = 10 min.

Solution:

S1 ---> 54 kmph,
S2 ---> 45 kmph

S1 means in 60 min bus travel 54 km.
S2 means 60-t(required time).
S2(45) -----> (60-t)min.
1 min -----> s2/60 - t.
60 min -----> s2 * 60/60 - t = s1.
t = 45 * 60/54,
t = 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.

the formula of stoppage time per hour = difference between their average speed/Speed without stoppage

Hence ,(54-45)/54*60 = 10 minute.

Consider there are two different buses for each case going through the same route, one stops and the other does not.

1. The time taken by the length of the journey is NOT necessary to calculate, eventually question is only asking for a given period of an hour, which means the distance would be different between the 2 cases.

2. The last line of the question says "For how many minutes does the bus stop per hour", this means stopping time is a part of "an hour",
and the two cases are as follows:

i) 45 km/hr=> 60 min = stopping time + travel time.
ii) 54 km/hr => 60 min = travel time.

3. In 1 hr, the distance covered in the first case is less, as the travel time is < 60 min and accordingly the speed is less(=45 km/hr). d1 = 45 km/hr * 1hr = 45 km.

Similarly, in 1 hr, the distance covered in the second case is more, as the time travelled is =60 min and therefore the speed is higher (=54 km/hr).
d2 = 54 km/hr * 1hr.
= 54 km.

4. Now, d2 - d1 = 54 - 45 = 9 km is the extra distance that bus 2 travels in 1 hour, which bus 1 could have travelled if it had no stopping time.

Now, stopping time can be easily calculated by determining how much extra time bus 2 takes to travel 9 km at its speed.

Stopping time = Distance/Speed = (9 km/54 km/hr) = (1/6) hr = 10 min.

Speed1 = 54kmp
Speed2 = 45kmph
By ratio method:
Speed diff is 9kmph.
It means the distance is 9 km.
Time = distance/speed
t = 9/54 = 1/6 hr.
Time = 10 min.