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# John is walking east at a speed of 3 miles per hour, while Bob is also

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
John is walking east at a speed of 3 miles per hour, while Bob is also  [#permalink]

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26 Mar 2019, 05:27
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:22) correct 17% (02:10) wrong based on 58 sessions

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John is walking east at a speed of 3 miles per hour, while Bob is also walking east, but at a speed of 5 miles per hour. If Bob is now 1 mile west of John, how many minutes will it take for Bob to catch up to John?

(A) 30
(B) 50
(C) 60
(D) 90
(E) 120

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Re: John is walking east at a speed of 3 miles per hour, while Bob is also  [#permalink]

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26 Mar 2019, 06:49
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Top Contributor
Bunuel wrote:
John is walking east at a speed of 3 miles per hour, while Bob is also walking east, but at a speed of 5 miles per hour. If Bob is now 1 mile west of John, how many minutes will it take for Bob to catch up to John?

(A) 30
(B) 50
(C) 60
(D) 90
(E) 120

This is a shrinking gap question

Bob is now 1 mile west of John
So, the gap = 1 mile

John is walking east at a speed of 3 miles per hour, while Bob is also walking east, but at a speed of 5 miles per hour.
5 mph - 3 mph = 2 mph
So, the gap SHRINKS at a rate of 2 mph

How many minutes will it take for Bob to catch up to John?
time = distance/rate
= 1 mile/2 mph
= 1/2 hours
= 30 minutes

Cheers,
Brent
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Re: John is walking east at a speed of 3 miles per hour, while Bob is also  [#permalink]

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26 Mar 2019, 07:56
Differential speed (as they travel in the same direction) between Bob and John is 2 mile per hour and the distance to cover is 1 mile. Hence 1/2 hours option A

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Re: John is walking east at a speed of 3 miles per hour, while Bob is also  [#permalink]

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26 Mar 2019, 11:22
Bunuel wrote:
John is walking east at a speed of 3 miles per hour, while Bob is also walking east, but at a speed of 5 miles per hour. If Bob is now 1 mile west of John, how many minutes will it take for Bob to catch up to John?

(A) 30
(B) 50
(C) 60
(D) 90
(E) 120

relative speed = 5-3 = 2 mph
distance = 1
so time 1/2 ; 0.5 * 60 ; 30 mins
IMO A
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Re: John is walking east at a speed of 3 miles per hour, while Bob is also  [#permalink]

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27 Mar 2019, 19:10
Bunuel wrote:
John is walking east at a speed of 3 miles per hour, while Bob is also walking east, but at a speed of 5 miles per hour. If Bob is now 1 mile west of John, how many minutes will it take for Bob to catch up to John?

(A) 30
(B) 50
(C) 60
(D) 90
(E) 120

Letting t = the time it will take for Bob to catch up to John, we can create the distance equation:

3t + 1 = 5t

1 = 2t

1/2 = t

We see that t = 1/2 hour or 30 minutes.

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Re: John is walking east at a speed of 3 miles per hour, while Bob is also   [#permalink] 27 Mar 2019, 19:10
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