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Katie passed a milestone on a highway while traveling back to her home

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Katie passed a milestone on a highway while traveling back to her home [#permalink] New post   13 Jan 2024, 00:57
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Katie passed a milestone on a highway while traveling back to her home at a constant speed of 50 miles per hour. Fifteen minutes later, Jack passed the same milestone traveling at a constant speed of 60 miles per hour while going in the same direction that Katie is going. If both Katie and Jack maintained their speeds and both remained on the highway, how long, in minutes, after Jack passed the milestone did the distance between Jack and Katie equal 10 miles?

Indicate all possible answers.


(A) 10
(B) 15
(C) 60
(D) 135
(E) 150

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Re: Katie passed a milestone on a highway while traveling back to her home [#permalink] New post   17 Jan 2024, 22:05
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Since Katie continued to travel in the 15 minutes after she passed the milestone, the distance she traveled in that 15 minutes is
\(15 minutes * \frac{1 hour }{ 60 minutes} * 50 miles per hour = 12.5 miles\)

Let h = time in hours after Jack passed the milestone.

Attachment:
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There are 2 ways that the distance between Jack and Katie equals 10 miles:
1) Jack is behind Katie by 10 miles
\(60h + 10 = 12.5 + 50h\)
\(10h = 2.5\)
\(h = \frac{2.5}{10} = \frac{1}{4}\)
Multiply by 60 to get 15 minutes.

2) Katie is behind Jack by 10 miles (since Jack's speed is faster, he will eventually surpass her)
\(60h = 12.5 + 10 + 50h\)
\(10h = 22.5\)
\(h = 2.25\)
Multiply by 60 to get 135 minutes.
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Re: Katie passed a milestone on a highway while traveling back to her home [#permalink]
17 Jan 2024, 22:05
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