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# Two friends phil and andrew started running simultaneously from a poin

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Senior Manager
Joined: 13 Jun 2013
Posts: 274
Two friends phil and andrew started running simultaneously from a poin  [#permalink]

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15 Nov 2014, 07:22
1
8
00:00

Difficulty:

75% (hard)

Question Stats:

62% (02:48) correct 38% (03:28) wrong based on 124 sessions

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Two friends phil and andrew started running simultaneously from a point P in the same direction along a straight running track. The ratio of speeds of phil and andrew was 2:5. Two hours later, andrew turned back and started running running backwards at one-fifth of his original speed. He met phil at a distance of 10 km from the point P. what was phil's running speed ?

A) 1.25 km/hr
B) 2.25 km/hr
C) 2.5 km/hr
D) 3.75 km/hr
E) 6.25 km/hr
Manager
Joined: 23 Oct 2014
Posts: 86
Concentration: Marketing
Re: Two friends phil and andrew started running simultaneously from a poin  [#permalink]

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15 Nov 2014, 19:05
So this is my method. If Phil and Andrew's speed ratio is 2:5 then...

Phil's Rate: 2x <- Note that this is what we need to solve for.
Andrew's Rate: 5x

For two hours they are running until Andrew turns around and goes back at 1/5 his speed. His speed will now 5x/5 = x. t=time spent after Andrew turns back.

Rate*Time of first two hours + Rate after Andrew turns back*Time spent running after Andrew turns back = 10 Km

Phil: 2x(2 Hours) + 2x (t Hours) = 10km
Andrew: 5x(2 Hours) -x (t Hours) = 10km <- You subtract xt because Andrew starts running backwards.

Phil Distance (10km) = Andrew Distance (10km)
2x(2) + 2xt = 5x(2) - xt
4x + 2xt = 10x - xt
3xt = 6x
t=2; they both spent 2 additional hours moving after Andrew decides to go backwards. Plug this into either Phil or Andrew's distance equation.

5x(2) - xt = 10
10x - (2)x = 10
8x = 10
x = 1.25

Since Phil's running speed is 2x; 2(1.25) = 2.5 km/hr
Senior Manager
Joined: 13 Jun 2013
Posts: 274
Re: Two friends phil and andrew started running simultaneously from a poin  [#permalink]

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16 Nov 2014, 08:13
well, this question is actually taken from the local newspaper. so, i don't have any official solution for it. but, this is how i solved this problem.

let speed of andrew is x. then speed of phil is (2/5)x
also, the distance traveled by andrew in 2 hours will be 2x, and in the same two hours. phil will travel (2/5)x*2=4/5x
this situation is depicted below. PC=2x PD=4/5x and DC= 2x-4/5x=6/5x

P------------------D----------------------C
now, when andrew is at C, phil is at point D. at this moment, phil start moving backward at the rate of x/5.
since the speed of phil is twice the new speed of andrew. therefore, the distance traveled by phil at the point, where they meet will be twice the distance traveled by andrew.
P------------------D-----------t-----------C
let the distance traveled by andrew from c to the meeting point t be k. therefore dt=2k
thus k+2k=6/5x
or k=2/5x
thus pt=pd+dt= 4/5x+4/5x=8/5x
also, as per the question pt=10. thus 8/5x=10
or x=50/8
thus phil's speed will be 2/5(50/8)=10/4=2.5km/hr
Senior Manager
Joined: 18 Jan 2010
Posts: 251
Re: Two friends phil and andrew started running simultaneously from a poin  [#permalink]

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22 Jun 2016, 05:55
1
manpreetsingh86 wrote:
Two friends phil and andrew started running simultaneously from a point P in the same direction along a straight running track. The ratio of speeds of phil and andrew was 2:5. Two hours later, andrew turned back and started running running backwards at one-fifth of his original speed. He met phil at a distance of 10 km from the point P. what was phil's running speed ?

A) 1.25 km/hr
B) 2.25 km/hr
C) 2.5 km/hr
D) 3.75 km/hr
E) 6.25 km/hr

let speed of Phil was 2x and that of Andrew was 5x.

They move in same direction. relative speed = 3x.

In two hours distance between two = 3x * 2 = 6x.

Now Andrew turns back. His speed is now x.

Now both runners will have a relative speed : 2x+x = 3x.

The two runners will meet, when the distance between them = 6x is exhausted.

this will be done in 2 hours.

Now in initial 2 hours + these 2 hours Phil ran:

2x * 4 hours = 8x distance

8x = 10
x = 10/8 = 1.25.

Phil's speed = 2x = 2.5.

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Joined: 09 Sep 2013
Posts: 10612
Re: Two friends phil and andrew started running simultaneously from a poin  [#permalink]

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21 Jul 2017, 10:49
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Re: Two friends phil and andrew started running simultaneously from a poin   [#permalink] 21 Jul 2017, 10:49
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