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

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Bunuel
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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ [#permalink] New post   20 Feb 2020, 05:08
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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] New post   20 Feb 2020, 06:35
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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
Answer: Option B

For Concept of Relative Speed, please refer to this Video


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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ [#permalink] New post   20 Feb 2020, 13:55
Answer is D:

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.
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Re: Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ [#permalink] New post   20 Feb 2020, 20:52
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
Answer: Option B

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] New post   22 Feb 2020, 01:46
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
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Re: Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ [#permalink] New post   19 Apr 2023, 19:46
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Re: Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ [#permalink]
19 Apr 2023, 19:46
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