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# Tricky question of Time speed & distance- STOPPAGE TIME ?

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Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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10 Jun 2011, 12:47
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A person travel 285 km in 6 hour. The part it travel by bus at 40 km/hr which include stoppage time of 10%. Second part is travel by train at 55 km/hr. Find Stoppage time?

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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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Updated on: 10 Jun 2011, 21:14
MrMicrostrip wrote:
A person travel 285 km in 6 hour. The part it travel by bus at 40 km/hr which include stoppage time of 10%. Second part is travel by train at 55 km/hr. Find Stoppage time?

Not sure .. I get 13 minutes.

t hrs @ 40km/hr + (6-1.1t) hrs @ 55 km/hr = 285km

solve for t ; t~ 2.2; 10 % = .23H = .23*60 = ~13 minutes

Originally posted by sudhir18n on 10 Jun 2011, 13:01.
Last edited by sudhir18n on 10 Jun 2011, 21:14, edited 2 times in total.
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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10 Jun 2011, 13:46
MrMicrostrip wrote:
A person travel 285 km in 6 hour. The part it travel by bus at 40 km/hr which include stoppage time of 10%. Second part is travel by train at 55 km/hr. Find Stoppage time?

Person traveled for time t in bus @ 40km/h
Distance=40t

time spent in the stoppage 0.1t
Distance=0*0.1t=0

Total time in bus+stoppage=1.1t

Time spent in train=6-1.1t
Distance traveled by train=50(6-1.1t)

Total Distance=285

$$40t+50(6-1.1t)=285$$
$$t=1$$
$$Stoppage=0.1h=6 minutes$$
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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10 Jun 2011, 13:53
fluke wrote:
MrMicrostrip wrote:
A person travel 285 km in 6 hour. The part it travel by bus at 40 km/hr which include stoppage time of 10%. Second part is travel by train at 55 km/hr. Find Stoppage time?

Person traveled for time t in bus @ 40km/h
Distance=40t

time spent in the stoppage 0.1t
Distance=0*0.1t=0

Total time in bus+stoppage=1.1t

Time spent in train=6-1.1t
Distance traveled by train=50(6-1.1t)

Total Distance=285

$$40t+50(6-1.1t)=285$$
$$t=1$$
$$Stoppage=0.1h=6 minutes$$

Train speed is 55km/hr .. i guess u have a typo?
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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10 Jun 2011, 14:11
1
sudhir18n wrote:
Train speed is 55km/hr .. i guess u have a typo?

Oh yea; there is!!!

$$285=40t+55(6-1.1t)$$
$$285=40t+330-1.1*55t$$
$$285=40t+330-60.5t$$
$$19.5t=45$$
$$t=\frac{45}{19.5}$$
$$Stoppage=\frac{45}{195}hour \approx 15min$$
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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10 Jun 2011, 18:27
Agree ...approx 15 mins
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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12 Jun 2011, 11:24
thanx friends for such an effort but ANSWER is 18 minutes.
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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12 Jun 2011, 11:44
Please post the solution for 18 mins
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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12 Jun 2011, 13:29
achingupta wrote:
It cannot be 18.

Stoppage time = 18 => total travel time @ 40Kmph including stoppage time = 180 min.

So total distance covered @ 40kmph => 40 * (180 - 18min) / 60(to convert in hr) = 108

=> distance remaining to be covered in (6hr - 180min = 3 hr) is 285 - 108 = 177

=> speed = 177/3 => 59kmph which is not same as 55kmph.

Can you please quote the source of this Q

I agree. Official explanation will help us resolve the discrepancy.
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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13 Jun 2011, 12:34
2
MrMicrostrip wrote:
A person travel 285 km in 6 hour. The part it travel by bus at 40 km/hr which include stoppage time of 10%. Second part is travel by train at 55 km/hr. Find Stoppage time?

The wording here is a little questionable. The journey had two parts: first part (including the stoppage time) and second part. It should be clarified that the 'average speed' during the first part is 40 km/hr (which accounts for the stoppage time in its calculation). I did assume that this is what the question meant since it says "at 40 km/hr which includes stoppage time of 10%", still I wasn't entirely sure whether it means that the 'first (btw, this word is missing) part of the journey' includes stoppage time or 'calculation of 40 km/hr' includes stoppage time. Anyway, assuming that it means the stoppage time is accounted for in the calculation of 40 km/hr,

Average speed during the entire journey = 285 km/6 hrs = 47.5 km/hr
Since 47.5 is exactly in the middle of 40 and 55, time taken to cover first part = time taken to cover second part (when calculating the weighted average of speed, time is the 'weight')
Hence time taken to cover first part = 6/2 hrs = 3 hrs.
Stoppage time = 10% of 3 hrs = 10% of 180 mins = 18 mins
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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13 Jun 2011, 13:23
VeritasPrepKarishma wrote:
MrMicrostrip wrote:
A person travel 285 km in 6 hour. The part it travel by bus at 40 km/hr which include stoppage time of 10%. Second part is travel by train at 55 km/hr. Find Stoppage time?

The wording here is a little questionable. The journey had two parts: first part (including the stoppage time) and second part. It should be clarified that the 'average speed' during the first part is 40 km/hr (which accounts for the stoppage time in its calculation). I did assume that this is what the question meant since it says "at 40 km/hr which includes stoppage time of 10%", still I wasn't entirely sure whether it means that the 'first (btw, this word is missing) part of the journey' includes stoppage time or 'calculation of 40 km/hr' includes stoppage time. Anyway, assuming that it means the stoppage time is accounted for in the calculation of 40 km/hr,

Average speed during the entire journey = 285 km/6 hrs = 47.5 km/hr
Since 47.5 is exactly in the middle of 40 and 55, time taken to cover first part = time taken to cover second part (when calculating the weighted average of speed, time is the 'weight')
Hence time taken to cover first part = 6/2 hrs = 3 hrs.
Stoppage time = 10% of 3 hrs = 10% of 180 mins = 18 mins

Karishma!!!

Do you create questions for official GMAT also? If yes, please PM me.
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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13 Jun 2011, 15:01
40t+55(6-t)=285 hence t=3 or 180 minutes

10/100*180 equals 18 minutes.
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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13 Jun 2011, 19:58
fluke wrote:
Karishma!!!

Do you create questions for official GMAT also? If yes, please PM me.

I certainly wish I did fluke!
It's a whole different story that had I been creating questions for GMAC, I would not have appeared on any public forum ever!
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?  [#permalink]

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20 Oct 2019, 11:43
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Re: Tricky question of Time speed & distance- STOPPAGE TIME ?   [#permalink] 20 Oct 2019, 11:43
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