Excluding stoppages, speed of the bus is 54 kmph and including stoppag

Question

Excluding stoppages, speed of the bus is 54 kmph and including stoppages it is 45 kmph. For how many minutes does the bus stop per hour?

A. 4
B. 6
C. 8
D. 10
E. 12

TestPrepUnlimited · Answer

Set the time it stopped as x minutes per hour, then for each hour the bus was not stopping for 60 - x minutes. The total distance in that hour would be  54*(60 - x)  in 60 minutes, so the average speed including the stops would be:

\frac{54*(60 - x)}{60} = 45

1 - \frac{x}{60} = \frac{45}{54} = \frac{5}{6}

\frac{x}{60} = \frac{1}{6}

x = 10

Ans: D

(Note we are allowed to use minutes because we are using ratios)

ScottTargetTestPrep · Answer

Solution:

We can let the distance that the bus travels be 45 km. Therefore, with stoppages, it takes the bus 1 hour to complete the distance. However, without stoppages, it only takes 45/54 = 5/6 hour = 50 minutes for the bus to complete the same distance. Therefore, the bus must stop for 10 minutes per hour.

Alternate Solution:

Let the distance be d. Then, the travel time, excluding stoppages, is d/45, and the travel time, including stoppages, is d/54. Thus, the total stoppage time is d/45 - d/54 = 6d/270 - 5d/270 = d/270. Since the total time with stoppages is d/45 and since the total stoppage time is d/270, the bus stopped (d/270)/(d/45) = 45/270 = 1/6 hour = 10 minutes per hour.

Answer: D

ZulfiquarA · Answer

My route:
Divide the numbers 45/54=5/6
Formula: S*T=D
45*6=270
54*5=270
Difference is 1 hour or 60 minutes
Time taken for every stop= 60/6=10  (D)

Fdambro294 · Answer

Normally without stopping:

In 60 minutes —————-> bus can travel 54 km

Thus, without stopping and constantly driving:

In 1 min ————-> bus can travel (54/60) = 9/10 km

Then we are told when the bus stops, in 60 minutes (1 hour), it is only able to cover 45 km

We can find the amount of time the bus spends driving in that 60 minutes. The rest of the time must have been spent stopping.

So over the course of this 1 hour (60 min):

If in 1 min while driving —————> bus can travel (9/10) km

Then in M minutes ————> bus is able to travel 45 km

1 / (9/10) = M / 45

M = 45 / (9/10)

M = 450 / 9

M = 50 minutes

This means the over the course of the 1 hour when the bus makes the stops, it must have spent 50 minutes driving at its usual speed.

The other 10 minutes must have been when the bus was stopped.

(D) 10 minutes

Posted from my mobile device

ArpySarker · Answer

54 km without stopping in 60 
45 km with stopping in 60min

length of stopping platforms = 54-45= 9km

it can travel 54km in 60 min
 9km in (60*9)/54 min =10 minutes

Alexdb10 · Answer

I've seen a couple of these questions pop up and I saw a really helpful method in another forum so I thought I'd share:

54kph without stoppages
45kph with stoppages

54-45=9

9km of distance is lost

therefore the bus is halted for 9/54 or 1/6 hours: 10 minutes per hour

WiziusCareers1 · Answer

Approach 1: The "Distance Gap" Method (Conceptual) 
This method focuses on how much distance is lost due to the stops.

Analyze the distance in one hour:
If the bus does not stop, it covers 54 km in 60 minutes.
If the bus does stop, it only covers 45 km in 60 minutes.

Calculate the "Lost" Distance:
The bus covered 9 km less than its full potential (54−45=9 km).

Calculate the time required to cover that gap:
We need to find out how long it takes the bus to travel those "lost" 9 km when it is actually moving at its normal speed (54 kmph).

Time = Distance/Speed
Time = 9/54 = 1/6 hour

Convert to minutes:
1/6 × 60 minutes =10 minutes

Conclusion: The 10 minutes the bus would have spent driving those 9 km were instead spent at a standstill.

Approach 2: The Speed Ratio Formula 
There is a direct formula used for "stoppage" problems that helps you get the answer in seconds:

Stop time per hour = {(Fast Speed−Slow Speed)/Fast Speed} * 60
 = {(54 - 45)/54} * 60
 = 10 minutes

Adit_ · Answer

Many ways to solve. You can simply subtract and take wrt to 54 like profit and loss problems. I like it super intuitive like this:

Take 54km total distance
1st takes 1hr
2nd takes 1.2 hrs or 12 mins extra
This 12 mins extra is for a period of 72 mins
Hence for per hour it is 12/72*60 = 10 mins

Excluding stoppages, speed of the bus is 54 kmph and including stoppag

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Excluding stoppages, speed of the bus is 54 kmph and including stoppag

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards