Aptitude - Time and Distance - Discussion

Let's we take that a bus reach an 54 km distance in 1 hour without any stoppages while the bus was covered 45 distance with some stop.

So we can understand that the remaining 9 kms were not reached the bus.
So, 9 km travelling time will be a stop time. We all know that, time=9/54*60=10 mins.

The easy method: For 1 hour the bus travels for 54 km then for one min its 54/60=0.9km.

So if the bus stops for one minute it travel 0.9 km less so if the bus travels 9 km less then it might stopped for 10 min.

Min per hour= (difference of two speeds÷ without stoppage)*60.
Or
Min per hour=(diff of two speeds÷ large number)*60.

Let me try it in my way
A Particular Distance is travelled by the Bus at 54kmph

When stoppages are included, 54 kmph turns to 45kmph in order to compensate the increase in time.

Let Distance = D, time = t, increase in time = x

D = 54 * t ---> (1)
D = 45 * (t + x) ---> (2)

Equating (1) & (2)

54t = 45 (t+x).
54t = 45t + 45x,
9t = 45x,
9t/45 = x,
(1/5) t = x,
t = 5x.


We need to find x for 1 hr (60 mins)
i.e t+x = 60.
5x+x = 60.
6x = 60.
X = 10.

(Some friends are getting 12mins instead of 10 mins because they are taking (t = 60 min) but (t +x = 60) is the correct one.

@Naren.

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

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.

Why to consider 54 rather than 45?

Well thought by Jaya ans Kushal. Gr8 guys!!

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.

@Ravi.

We have been given speeds with stoppages and without stoppages,i.e., 45KM/h(with stoppages) and 54 Km/h( without stoppages).

Now, the question wants us to find that how much time is consumed in those stoppages.

Here the value of speed is based upon the time it took to reach a particular distance.

So naturally with stoppages the time will be more so for same distance the average speed is reduced i.e., 45Km/h.

Without stoppages, speed will be 54km/h.

Now consider the time to be one hour.Why one hour, because question wants us to find the minutes the bus stop per hour. Per hour.

So what is the distance for One hour at 54km/h and 45km/h?

Distance = 54KM and 45KM.
Now, what is the difference between these two?
9Km.
This is done to find what stoppages cost in term of distance between two buses.

Now, why 54Km?
Since you already know the difference in distance due to stoppages you need to use the speed with which the bus is covering that stoppage distance.

So,
9/54 = 1/6hr.
To convert this into minute just multiply it with 60 and you will have a number of minutes.,i.e., 10 Mins.

Is it clear now Ravi?