Aptitude - Time and Distance - Discussion

@All.

Consider the distance is only 54 kms. At 54 kmph it will take only 1 hr.
But since due to stoppages it takes 10 minutes extra (the time of stoppages).
So, shouldn't we get 45 kmph if we divide 54 km the distance by 1 hr 10 minutes (70 minutes)? We don't get that, of course. The bus runs at 54 and with the stoppage, rit reaches 45 km. 9 km is remaining. The average speed with stoppages was 45kmph. the remaining distance of 9 km has to be completed by that average speed as there are no more stoppages to get the correct time taken by the bus and not by 54kmph.

So, it will work out to be 12 minutes, not 10 minutes.

Thanks for explaining @Anoo.

54km -------- 60min
9km ----------- ?min


Then, 9km÷54km * 60min = 10mints.

Why we take 54 instead of 45? Please explain.

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

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.

@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.

Non stoppages speed= 54kmph,
with stoppages speed= 45kmph.

Reduce speed due to stoppages = 54-45 = 9 kmph.
we need to find the time taken by bus at a stop in each hour i.e t
t = s/v,
t = 9/54 ph ( we take 54 because we are talking about non-stoppages).
= 1/6 *60 min.
=10 min.

Bus travels at 54 km/hr.
Due to stoppages say t min, it travels only for (60-t) min.
(60-t) min= (60-t)/60 hr,
Given average speed = 45 km/hr,
Average speed = distance travelled/ total time taken.

45 = (54*(60-t)/60)/1 hr.
45 = 9*(60-t)/10,
450 = 540-9t,
t = 90/9 = 10 min.

The bus travelled only 45kms. Hence, it would be correct to divide 45 (and not 50) and multiply 60 with 9 kms (less travelled).

Am I right? please clarify for me.