Aptitude - Time and Distance - Discussion

We are taking 9/54, because car is moving @ 54 not 45 km/hr. The question is on average speed which means total distance divided by total time.

Now, because car waits for some minutes at stops that is why average speed gets decreased. So, speed is same which is 54 km/hr, but including stoppages total time has increased. Therefore average speed comes down.

For 60 min......54 kmph so.

For ? min.......45 kmph.

= 45*60/54 = 50 mins it means 10 mins less so it has stopped for 10 mins.

There is a formula for this questions:

(V1-v2)/v1.

V1= Without stoppage velocity.

V2 = With stoppage.

Result is in hour. Multiply by 60 to get minutes.

How can you take if t=1 randomly?

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.

I will suggest one more formula to solve this kind of problems when stoppage time has to be calculated.

Then, stoppage time = 1-Slower speed/Faster speed.

Hence in this case.

= 1-45/54.
= 1- 5/6.
= (6-5)/6.
= 1/6.

Which can be converted to = 1/6*60 = 10 min.

Please explain in min to sec and min to hours.

Why we are considering 54 kmph rather 45 kmph?

To all those who have doubt why 54 kmph is considered. The problem is to find how many minutes does the bus stops in stoppages.

54 kmph means it travels 54 km per a single hour (i.e 60 min) excluding stoppages.

Including stoppages speed reduced to 45 km per a single hour. It means per one hour due to stoppages there is 9 km loss per a single hour.

We should take 54 kmph because we should know what time it takes for bus for a km. So 54 km-->60 min then 1 km-->60/54 min.

For 9 km--> (9*60) /54 = 10 min.

Why we are considering 54 kmph rather 45 kmph?