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# Anne passes by a church while driving at 48 miles per hour. 40 minutes

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Anne passes by a church while driving at 48 miles per hour. 40 minutes [#permalink]
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Given:
1. Anne passes by a church while driving at 48 miles per hour.
2. 40 minutes later, Jack passes by the same point, driving in the same direction as Anne’s, at 64 miles per hour.

Asked: If Anne and Jack continue to drive for the next six hours in the same direction at the same speeds, after how much time of Anne’s passing by the church will Jack cross her?

Distance travelled by Anne after k hours after crossing the church = 48k
Distance travelled by Jack after k hours of crossing the church by Anne = 64(k-40/60) = 64k - 128/3
Since Jack crosses Anne
48k = 64k - 128/3
16k = 128/3
k = 2 2/3 hours = 2 hours 40 minutes

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Re: Anne passes by a church while driving at 48 miles per hour. 40 minutes [#permalink]
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jn0r wrote:
Anne passes by a church while driving at 48 miles per hour. 40 minutes later, Jack passes by the same point, driving in the same direction as Anne’s, at 64 miles per hour. If Anne and Jack continue to drive for the next six hours in the same direction at the same speeds, after how much time of Anne’s passing by the church will Jack cross her?

A) 30 minutes
B) 1 hour 20 minutes
C) 2 hours
D) 2 hour 40 minutes
E) 3 hours

Solution:

Let’s let t = the number of hours Anne will have driven when she and Jack cross paths. Thus, Anne will have driven 48t miles.

Jack will have traveled 40 fewer minutes than Anne, which is ⅔ hour. Thus, Jack’s time is (t - ⅔), and so his total distance will be 64(t - ⅔).

Because each person will have driven the same number of miles, we can equate the two expressions for their distances:

48t = 64(t - ⅔)

48t = 64t - 128/3

128/3 = 16t

(128/3) / 16 = t

2 ⅔ = t

Thus, the two will cross paths after 2 ⅔ hours, or 2 hours 40 minutes.

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Re: Anne passes by a church while driving at 48 miles per hour. 40 minutes [#permalink]
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Re: Anne passes by a church while driving at 48 miles per hour. 40 minutes [#permalink]
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