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# Xavier starts from P towards Q at a speed of 30 kmph and after every 1

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Intern
Joined: 08 Jan 2015
Posts: 12
Xavier starts from P towards Q at a speed of 30 kmph and after every 1  [#permalink]

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20 Jan 2015, 04:27
3
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:22) correct 33% (02:53) wrong based on 126 sessions

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Xavier starts from P towards Q at a speed of 30 kmph and after every 12 mins increases his speed by 5 kmph. If the distance between P and Q is 51km, then how much time does he take to cover the distance?
A) 60 mins
B) 72 mins
C) 90 mins
D) 120mins
E) 100mins
Senior Manager
Joined: 13 Jun 2013
Posts: 276
Re: Xavier starts from P towards Q at a speed of 30 kmph and after every 1  [#permalink]

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22 Jan 2015, 02:19
1
abdulfmk wrote:
Xavier starts from P towards Q at a speed of 30 kmph and after every 12 mins increases his speed by 5 kmph. If the distance between P and Q is 51km, then how much time does he take to cover the distance?
A) 60 mins
B) 72 mins
C) 90 mins
D) 120mins
E) 100mins

Distance traveled by xavier in the initial 12 minutes = 30(12/60) =6
after these initial 12 minutes, xavier increases his speed by 5 km/h, thus his new speed becomes 35 km/h
now distance traveled in next 12 minutes = 35(12/60) = 7

now, his new speed becomes 40km/h, therefore distance traveled in 12 min. with this speed = 40(12/60) =8

as we can see that after every 12 minutes distance traveled by xavier increases by 1 unit, therefore instead of calculating the distance covered in every 12 minutes we can just simply add the distance from 6 onward and can stop when the sum becomes 53.

thus we have 6+7+8+9+10+11 =53, as the number of values used to make this sum a total of 53 is 6. hence total time taken = 12.(6) = 72 minutes.
VP
Joined: 07 Dec 2014
Posts: 1104
Xavier starts from P towards Q at a speed of 30 kmph and after every 1  [#permalink]

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15 Jun 2016, 09:29
let t=number of 1/5 hour segments needed
t=51/[(t+11)/2]
t=6
6*1/5=6/5 hours=72 minutes
Director
Joined: 20 Feb 2015
Posts: 793
Concentration: Strategy, General Management
Re: Xavier starts from P towards Q at a speed of 30 kmph and after every 1  [#permalink]

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17 Jun 2016, 03:18
1st 12 minutes = 12/60 =1/5 hours
distance covered = 30*1/5 = 6 kilometres
2nd 12 minutes distance covered = 35*1/5 =7 Kilometres
3rd 12 minutes distance covered = 40*1/5=8 Kilometres
6+7+8+9+10+11=51
time taken = 12*6 = 72 minutes
Non-Human User
Joined: 09 Sep 2013
Posts: 8461
Re: Xavier starts from P towards Q at a speed of 30 kmph and after every 1  [#permalink]

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25 Sep 2017, 12:15
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Re: Xavier starts from P towards Q at a speed of 30 kmph and after every 1 &nbs [#permalink] 25 Sep 2017, 12:15
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# Xavier starts from P towards Q at a speed of 30 kmph and after every 1

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