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Point P lies between points A and B such that the length of BP is thri

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Point P lies between points A and B such that the length of BP is thri  [#permalink]

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New post 03 Apr 2020, 05:46
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A
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C
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E

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Question Stats:

82% (03:03) correct 18% (02:59) wrong based on 51 sessions

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Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then what is the time, in minutes, taken by car 1 in reaching P from A?

A. 8
B. 9
C. 10
D. 11
E. 12


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Re: Point P lies between points A and B such that the length of BP is thri  [#permalink]

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New post 03 Apr 2020, 07:10
Let Total distance is D.
AP is X and BP is 3X
Speed of car A is S1
Speed of car B is S2 or S1/2
The time taken by car A for reaching P is Y
And time taken by Car B for reaching P is Y+1
So equations will be
Distance=speed*time
X=S1*Y----(1)
3X=S2*(Y+1)
3X=S1/2*(Y+1)
X=S1/6(Y+1)-----(2)
Equating both
S1*Y=S1/6(Y+1)
6S1*Y=S1*Y+S1
5*S1*Y=S1
Y=1/5 or 12 minutes. (60*1/5)
OA is E

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Re: Point P lies between points A and B such that the length of BP is thri  [#permalink]

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New post 04 Apr 2020, 11:56
Bunuel wrote:
Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then what is the time, in minutes, taken by car 1 in reaching P from A?

A. 8
B. 9
C. 10
D. 11
E. 12



Let Distance between A and P be 10m and B and P be 30m

Speed of Car 1: S1=10/T1 (T1 is the time taken by Car 1 to reach P)

Speed of Car 2: S2=30/T1+1 ( Given in the question that Car 2 takes one hour more than Car 1 to reach P)

Also, given S2=1/2 S1

We have, S1=10/T1 -(1)
S1= 60/(T1+1) -(2)

Solving these two equations we get, T1 = 1/5 hrs
Multiply 1/5 by 60 since the question is asking the time taken in minutes: 1/5 * 60 = 12 mins


Answer: (E)
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Re: Point P lies between points A and B such that the length of BP is thri  [#permalink]

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New post 05 Apr 2020, 21:56
Let AP be 1 km so BP is 3 km.
Let the time taken by Car 1 (C1) to reach P (i.e. travel 1 km) be T hrs. Then the time taken by C2 to reach P (i.e. travel 3 km) is (T+1) hr so the time C2 will need to travel 1 km will be (T+1)/3 km.
The ratio of the speeds of two moving objects is equal to the inverse of the times taken by each to cover the same distance. Thus:
(Speed of C1)/(Speed of C2) = (Time for C2 to cover 1 km)/(Time for C1 to cover 1 km)
2/1 = {(T+1)/3}/T....> 2/1 = (T+1)/3T.... T = 1/5 hr = 12 minutes. ANS: E
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Re: Point P lies between points A and B such that the length of BP is thri  [#permalink]

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New post 08 May 2020, 11:27
Bunuel wrote:
Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then what is the time, in minutes, taken by car 1 in reaching P from A?

A. 8
B. 9
C. 10
D. 11
E. 12


c1: takes t to reach ap=x
c2: takes t+1 to reach bp=3x

c1's time: x/r=t
c2's time: 3x/r/2=t+1
equate: 6x-x=r, r=5x

c1's time: 5x/x=1/5hr*60=12min

ans (E)
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Re: Point P lies between points A and B such that the length of BP is thri   [#permalink] 08 May 2020, 11:27

Point P lies between points A and B such that the length of BP is thri

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