Aptitude - Time and Distance - Discussion

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?

The average speed (including stoppage) is 45 km/hr.
Distance = (rate)(time).
So, in ONE hour, the distance traveled = (45)(1) = 45 km.

The average speed (excluding stoppage) is 54 km/hr.
At this speed, HOW long will it take the bus travel 45 km?
time = distance/rate.
So, time = 45/54.
= 5/6 hours,
= 50 minutes.

At a speed of 54 km/hr, the bus can travel 45 km every 50 minutes.
So, it must be motionless for the other 10 minutes.

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.

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.

@Sumit Dubey.

Use Arithmetic Progression (A.P.)
Sum to n-terms = n/2(2a + (n-1)d).
n/2 (2*40 + (n-1)5) = 385
40n + 5n^2/2 - 5n/2 = 385
5n^2 + 75n - 650 = 0
(5n - 35)(n + 21) = 0.

So,
n = 7 or n = -21.
As n (time) cannot be negative we will discard -21.
Hence, the answer is 7 hours.

How to get 9 km?

It is obtained by 54 kmph - 45 kmph = 9 kmph.

How did 9/54 come?

Hey its 54 kmph and 45 kmph. Can you explain how you got 9 km by subtracting the speeds of bus at different circumstances?