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# Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./

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Math Expert
Joined: 02 Sep 2009
Posts: 62353
Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./  [#permalink]

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20 Feb 2020, 04:08
00:00

Difficulty:

55% (hard)

Question Stats:

73% (02:00) correct 27% (02:05) wrong based on 21 sessions

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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference. After how many minutes are the three of them together again?

A. 3 mins
B. 5 mins
C. 7 mins
D. 10 mins
E. 15 mins

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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./  [#permalink]

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20 Feb 2020, 05:35
Bunuel wrote:
Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference. After how many minutes are the three of them together again?

A. 3 mins
B. 5 mins
C. 7 mins
D. 10 mins
E. 15 mins

Let,
Speed of A = 1 ft./sec
Speed of B = 3 ft./sec
Speed of C = 6 ft./sec

Relative Speed of A and B = 3-1 (Same direction) = 2 ft/Sec
Cyclic Time for them to come together = 300/2 = 150 secs

Relative Speed of A and C = 6-1 (Same direction) = 5 ft/Sec
Cyclic Time for them to come together = 300/5 = 60 secs

Relative Speed of A and B = 6-3 (Same direction) = 3 ft/Sec
Cyclic Time for them to come together = 300/3 = 100 secs

All three of them will be together when the time elapsed is a common Multiple of {150, 60, 100} = LCM {150, 60, 100} = 300 secs = 300/60 mins = 5 mins

For Concept of Relative Speed, please refer to this Video

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Joined: 04 Feb 2018
Posts: 2
Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./  [#permalink]

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20 Feb 2020, 12:55

Walking rates are 6o feet per min, 180 feer per min and 360 feet per min.

1) 60*time/300
2) 180*time/300
3) 360*time/300
So, 1), 2) and 3) should be integers.
Manager
Joined: 22 Sep 2018
Posts: 76
Re: Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./  [#permalink]

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20 Feb 2020, 19:52
GMATinsight wrote:
Bunuel wrote:
Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference. After how many minutes are the three of them together again?

A. 3 mins
B. 5 mins
C. 7 mins
D. 10 mins
E. 15 mins

Let,
Speed of A = 1 ft./sec
Speed of B = 3 ft./sec
Speed of C = 6 ft./sec

Relative Speed of A and B = 3-1 (Same direction) = 2 ft/Sec
Cyclic Time for them to come together = 300/2 = 150 secs

Relative Speed of A and C = 6-1 (Same direction) = 5 ft/Sec
Cyclic Time for them to come together = 300/5 = 60 secs

Relative Speed of A and B = 6-3 (Same direction) = 3 ft/Sec
Cyclic Time for them to come together = 300/3 = 100 secs

All three of them will be together when the time elapsed is a common Multiple of {150, 60, 100} = LCM {150, 60, 100} = 300 secs = 300/60 mins = 5 mins

For Concept of Relative Speed, please refer to this Video

Cant we directly calculate the time taken for each one to complete the round and then take the lcm of the times to get the required time ? I did so and got the same answer 5 min.
if doing so wrong in what case I may get the wrong answer ???
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Re: Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./  [#permalink]

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22 Feb 2020, 00:46
for three friends who are moving in same direction 300 feet ; the relative speed of all needs to be determined wrt to each other
Speed of A&B ; 2
A&C ; 5 and B&C ; 3
we get time ; 300/2 ; 300/5 ; 300/3 ; 150,60,100
LCM ; 300 sec
in mins ; 300/60 ; 5 mins
IMO B

Bunuel wrote:
Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference. After how many minutes are the three of them together again?

A. 3 mins
B. 5 mins
C. 7 mins
D. 10 mins
E. 15 mins
Re: Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./   [#permalink] 22 Feb 2020, 00:46
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