Aptitude - Time and Distance - Discussion

Speed is 54 km/hr, here clarity is speed is never reduced.

So in one hour, it covers 54 km without stopping, now since it has stopped it covered only 45 km at speed of 54 km/hr. had it not stopped it would have covered 54 kms, but it stopped hence it covered only 45 km.
Distance not covered is 54 - 45 = 9kms.
Now the time it would have taken to cover 9kms is (time = distance/speed)
Time reqd to cover 9 km @ 54km/hr = 9/54 = 1/6 hours i.e 10 minutes.

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.

Fast speed-slow speed/Fast Speed = 54-45/54 = 1/6.
To convert into minutes =1/6 * 60 = 10.

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.

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


Then, 9km÷54km * 60min = 10mints.

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

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

If he travels for 10 km.

54 kmph means 54x10= 540.
45 kmph means 45x10= 450.

Difference of distance 540-450=90km,
Difference of speed 54-45=9.
.Distance=speed x time.
90 = 9xtime,
time = 10.

S1 = 54kmph
S2 = 45kmph
T=?.

D = S2-S1=> 54 - 45 = 9km.

# Due to stoppages it travels 9km less than its usual distance,
Time = Distance/Speed.
= 9/54 (S2 speed is taken to calculate the stopping time)
=1/6hr.

# To convert hr to min "*" by 60=>(1/6)*60 = 10min.
Therefore it stops 10min every hour in stoppages
Time = speed/distance.

(Initial - final/initial) hours = covert to minute and get the answer.

@All.

Very easy approach:

S1 = 54.
S2 = 45.

By ratio method:
The speed diff is 9kmph.
distance = 9 km.
T= d/s.
t = 9/54 = 1/6 hr=(1/6) * 60min.
t = 10 min.