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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ 20 Feb 2020, 05:08
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69% (02:02) correct 31% (02:15) wrong based on 186 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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B
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Schools: IIM (A) ISB '24
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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ 20 Feb 2020, 06:35
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Bunuel
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
Show more

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./ 20 Feb 2020, 13:55
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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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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ 20 Feb 2020, 20:52
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Bunuel
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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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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Three friends-whose walking rates are 1 ft./sec., 3ft./sec., and 6ft./ 22 Feb 2020, 01:46
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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
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./ 14 Dec 2024, 07:31
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