Aptitude - Time and Distance - Discussion
Discussion Forum : Time and Distance - General Questions (Q.No. 5)
5.
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Answer: Option
Explanation:
Due to stoppages, it covers 9 km less.
| Time taken to cover 9 km = |  |
9 | x 60 |  min |
= 10 min. |
| 54 |
Discussion:
205 comments Page 5 of 21.
Mandy said:
8 years ago
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.
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.
(1)
Donald Trump said:
5 years ago
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.
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.
(1)
Joel said:
5 years ago
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.
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.
(1)
Harsh said:
4 years ago
@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.
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.
(1)
Kanmani said:
1 decade ago
How to get 9 km?
Sundar said:
1 decade ago
It is obtained by 54 kmph - 45 kmph = 9 kmph.
Girishkumar said:
1 decade ago
How did 9/54 come?
Shaju said:
1 decade ago
Hey its 54 kmph and 45 kmph. Can you explain how you got 9 km by subtracting the speeds of bus at different circumstances?
Nitesh85 said:
1 decade ago
@Mr.Shaju
54 - 45 = 9 km is absolutely correct because we are calculating relative results.
54 - 45 = 9 km is absolutely correct because we are calculating relative results.
Nitesh Nandwana said:
1 decade ago
@Girishkumar hi itz simple.
Because 54km in 1 hour.
So 1 km in 1/54 hour.
So 9 km in 9* (1/54) *60 min (1 hour = 60 min).
Because 54km in 1 hour.
So 1 km in 1/54 hour.
So 9 km in 9* (1/54) *60 min (1 hour = 60 min).
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