Excluding the halts, the speed of the bus is 50 km/ hr and including

Question

Excluding the halts, the speed of the bus is 50 km/ hr and including the halts it is 40 km/hr. For how many minutes does the bus stop per hour?

A. 12
B. 14
C. 15
D. 18
E. 20

nushm · Accepted Answer

Let x be the number of minutes of halt.
Distance traveled in 1 hr excluding halt = 50*(60-x)
Distance traveled in 1 hr including halt = 40*60
Both distances are equal 
Hence, 50*(60-x) = 40*60
x = 60-48 = 12 mins
bus halted for 12 mins

mnk12 · Answer

Let total distance 200km
Without halt bus takes 200/50 = 4 hr
With halt bus takes 200/40 = 5 hr
Total extra time because of halt = 5-4=1hr
Now on a 5 hr journey, duration of halt = 1hr
So in 1 hr, duration of halt is 1/5 = 0.2hr or 12 min.

mcrea · Answer

I cannot wrap my head on the following is the right approach:
Distance traveled in 1 hr excluding halt = 50*(60-x)
Distance traveled in 1 hr including halt = 40*60

and the following is wrong:
Distance traveled in 1 hr excluding halt = 50*60
Distance traveled in 1 hr including halt = 40*(60+x)

can someone explain?

pierjoejoe · Answer

YOUR solution is completely fine, you have to be careful with the interpretation of t and x:

METHOD I

d is the same for both routes, in one route the speed is 50, the other 40
in the first route the bus takes t-x, in the other t.
   d 
 50 
 t-x 
 
  d 
 40 
 t

where t represent the total time the bus takes to travel the road  WITH  stops.
and x represent the amount of time spent at the stop in t hours of travel.
so 
d = 50*(t-x) 
d = 40t
50*(t-x) = 40t
thus x = t/5
meaning that if the total time travelling with stops is 1h, the total time for stops is x = 12 minutes

METHOD II

the same reasoning goes the same way around BUT be cautious of what t and x represent.
if we take:

d 
 50 
 t 
 
  d 
 40 
 t+x

d = 50t
d = 40(t+x)

now t represent the total time the bus takes to travel the road  WITHOUT  stops.
and x represent the amount of time spent at the stop in t+x hours of travel.

thus the relationship is 
x = t/4

SO NOW BE CAUTIOUS, because the total time travelling now is not t, but t+x

so if we travel a total of 1 hour --> t+x = 1
than given the relationship x = t/4 
t + 1/4t = 1
t * 5/4 = 1 
t = 4/5

now given 
t+x = 1h
t = 4/5 (total time travelling in t+x)

x = 1 - 4/5 = 1/5 of one hour, that is 12 minutes (total time stopped in t+x)

hope it is clearer, i could't wrap my head around it too, than it got me

iamjatinagrawal · Answer

Excluding the halts, speed  = 50 km/hr  
 Including the halts, speed  = 40 km/hr

Simple method to solve such a question: ((Excluding the halts speed-Including the halts)/Excluding the halts)*minutes in an hour

Hence, the answer is  ((50-40)/50)*60 = 12   minutes.

luisdicampo · Answer

Deconstructing the Question  
Speed excluding halts ( S_{fast} ) = 50 km/hr.
Speed including halts ( S_{slow} ) = 40 km/hr.
Target: Minutes the bus stops per hour.

Step 1: The "Lost Distance" Logic  
In a span of 1 hour:
- Without stopping, the bus would cover 50 km.
- With stops, the bus actually covers only 40 km.
The difference (shortfall) is  50 - 40 = 10  km.

Step 2: Calculate Time for Lost Distance  
The bus "lost" those 10 km because it was stationary. We need to find how long it takes to cover 10 km at its normal driving speed (50 km/hr).

ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} 
 	ext{Stop Time} = \frac{10 	ext{ km}}{50 	ext{ km/hr}} = \frac{1}{5} 	ext{ hours} .

Step 3: Convert to Minutes  
 \frac{1}{5} 	imes 60 	ext{ minutes} = 12 	ext{ minutes} .

Shortcut Formula:  
 	ext{Stop time per hour} = \frac{	ext{Difference in Speeds}}{	ext{Speed without stops}} 	imes 60 
 = \frac{50 - 40}{50} 	imes 60 = \frac{10}{50} 	imes 60 = 12  min.

Answer:  A

egmat · Answer

Looking at your doubt, I can see the confusion about what "including halts" means. Let me clarify this key concept!

The Core Issue: 
You're misunderstanding what the  40 km/hr  speed "including halts" represents.

Common Mistake:  Thinking that "including halts" means the bus travels for MORE time ( 60+x  minutes)

Correct Understanding:  "Including halts" means the  40 km/hr  is an  average speed  calculated over the  same 60-minute period , where the bus is stopped for part of that time!

Here's what actually happens: 
• In  1 hour  ( 60 minutes ), the bus stops for  x  minutes
• So it only moves for  (60-x)  minutes at  50 km/hr 
• Distance covered =  50 × (60-x)/60  km

The key insight:  The  40 km  distance "including halts" is the  total distance  covered in that  same 60-minute period  - not in  (60+x)  minutes!

Think of it like this: You have exactly  1 hour  to travel. During this hour:
• Part of the time you're moving at  50 km/hr 
• Part of the time you're stopped ( 0 km/hr )
• Your average speed for the whole hour is  40 km/hr

Therefore: 
 50 × (60-x)/60 = 40 
 x = 12 minutes

Answer: A (12 minutes)

Remember:  When a problem mentions speed "including stops," it's giving you the  average speed  over the total time period - the bus doesn't get extra time because it stopped!

Goutham999 · Answer

If the bus travels at 40km Avg speed with Halt.

In 1 Hour, the travelled distance become 40Km——- 1

If the Bus does not stop anywhere, it can cover the same 40Km distance in 40/50 Hrs (T=D/S)——- 2

We know,

Time of Halt=Time with Halt- Time without Halt

1-40/50=1/5

Therefore, 60*1/5 = 12 Mins

Excluding the halts, the speed of the bus is 50 km/ hr and including

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Excluding the halts, the speed of the bus is 50 km/ hr and including

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