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# Julia and Keaton are hiking on the same trail. Julia hikes at a rate

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Math Expert
Joined: 02 Sep 2009
Posts: 50060
Julia and Keaton are hiking on the same trail. Julia hikes at a rate  [#permalink]

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17 Apr 2018, 05:12
00:00

Difficulty:

25% (medium)

Question Stats:

86% (01:50) correct 14% (02:29) wrong based on 73 sessions

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Julia and Keaton are hiking on the same trail. Julia hikes at a rate of 3 miles per hour and starts hiking at 9:00 AM. If Keaton leaves at 9:30 and catches up with Julia at 12:30 PM, at what rate has Keaton been hiking, in miles per hour?

A. 1.5
B. 2.5
C. 3.5
D. 3.75
E. 4.0

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Re: Julia and Keaton are hiking on the same trail. Julia hikes at a rate  [#permalink]

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17 Apr 2018, 05:24
1
Bunuel wrote:
Julia and Keaton are hiking on the same trail. Julia hikes at a rate of 3 miles per hour and starts hiking at 9:00 AM. If Keaton leaves at 9:30 and catches up with Julia at 12:30 PM, at what rate has Keaton been hiking, in miles per hour?

A. 1.5
B. 2.5
C. 3.5
D. 3.75
E. 4.0

Distance is same for both Julia and Keaton.

Julia distance = 3*3.5 = 14 miles

Keaton speed = distance/time = 14/3 = 3.5 miles per hour

Hence option C = 3.5 is the answer.
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Re: Julia and Keaton are hiking on the same trail. Julia hikes at a rate  [#permalink]

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17 Apr 2018, 06:15
Bunuel wrote:
Julia and Keaton are hiking on the same trail. Julia hikes at a rate of 3 miles per hour and starts hiking at 9:00 AM. If Keaton leaves at 9:30 and catches up with Julia at 12:30 PM, at what rate has Keaton been hiking, in miles per hour?

A. 1.5
B. 2.5
C. 3.5
D. 3.75
E. 4.0

Julia starts hiking at $$9$$ and 'ends' at $$12.5$$. Thus, total time for Julia is $$12.5 - 9 = 3.5$$
$$Distance = Rate*Time = 3*3.5 = 10.5$$

Keaton starts hiking at $$9.5$$ and 'ends' at $$12.5$$. Thus, total time for Keaton is $$12.5 - 9.5 = 3$$
$$Distance = Rate*Time$$. => $$10.5 = x*3$$ => $$x = 3.5$$

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Re: Julia and Keaton are hiking on the same trail. Julia hikes at a rate  [#permalink]

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19 Apr 2018, 16:50
1
Bunuel wrote:
Julia and Keaton are hiking on the same trail. Julia hikes at a rate of 3 miles per hour and starts hiking at 9:00 AM. If Keaton leaves at 9:30 and catches up with Julia at 12:30 PM, at what rate has Keaton been hiking, in miles per hour?

A. 1.5
B. 2.5
C. 3.5
D. 3.75
E. 4.0

Since Julia and Keaton have each traveled the same distance when Keaton catches up with Julia at 12:30, we set their distances equal to each other in the equation. Letting Keaton’s rate = r, we have:

Julia’s distance = Keaton’s distance

3(3.5) = r(3)

3.5 = r

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Re: Julia and Keaton are hiking on the same trail. Julia hikes at a rate &nbs [#permalink] 19 Apr 2018, 16:50
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