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Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
 13 Oct 2012, 08:27
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Question Stats:
50% (02:42) correct
50% (02:17) wrong based on 3 sessions
Stacy and Katie plan to walk the 27-mile scenic route across Malibu, starting at opposite ends of the route at the same time. If Stacy's rate is 25% faster than Katie's, how far will Stacy have walked when they pass each other? A.12 B.13.5 C.15 D.16.25 E.17.33 Stacy's rate is 25% faster, meaning that she covers 5/4 as much distance over the same time. So for every 9 miles total that the two cover, Stacy covers 5 and Katie covers 4. With a 27-mile route, and 27 breaking into ninths (3 * 9), the math works out cleanly via this conceptual method: With a 5:4 ratio and three sets of 9 miles to cover, Stacy will cover 15 miles and Katie will cover 12.
Therefore, the correct answer is 15.
Alternatively, you can treat this as a problem with two variables and two solutions:
K + S = 27, and S = 5/4K
Solving for S, you’ll again find that S = 15. Press Kudos for this practice question  _________________
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Manager
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
14 Oct 2012, 05:49
thevenus wrote: Stacy and Katie plan to walk the 27-mile scenic route across Malibu, starting at opposite ends of the route at the same time. If Stacy's rate is 25% faster than Katie's, how far will Stacy have walked when they pass each other? A.12 B.13.5 C.15 D.16.25 E.17.33 Stacy's rate is 25% faster, meaning that she covers 5/4 as much distance over the same time. So for every 9 miles total that the two cover, Stacy covers 5 and Katie covers 4. With a 27-mile route, and 27 breaking into ninths (3 * 9), the math works out cleanly via this conceptual method: With a 5:4 ratio and three sets of 9 miles to cover, Stacy will cover 15 miles and Katie will cover 12.
Therefore, the correct answer is 15.
Alternatively, you can treat this as a problem with two variables and two solutions:
K + S = 27, and S = 5/4K
Solving for S, you’ll again find that S = 15. Press Kudos for this practice question Please help me in understanding as to where i went wrong. My approach is.. t = time taken D = total distance D s = distance covered by Stacy in time "t" D k = distance covered by Katie in time "t" S s = Speed of Stacy. S k = Speed of Katie. t = D s/S s = D k/S kt = [D-D k]/[(5/4)S k = D k/S kt = 4[27-D k]/5S k = D k/S k108 = 5D kBut answer that i got is wrong 
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
14 Oct 2012, 13:04
navigator123 wrote: thevenus wrote: Stacy and Katie plan to walk the 27-mile scenic route across Malibu, starting at opposite ends of the route at the same time. If Stacy's rate is 25% faster than Katie's, how far will Stacy have walked when they pass each other? A.12 B.13.5 C.15 D.16.25 E.17.33 Stacy's rate is 25% faster, meaning that she covers 5/4 as much distance over the same time. So for every 9 miles total that the two cover, Stacy covers 5 and Katie covers 4. With a 27-mile route, and 27 breaking into ninths (3 * 9), the math works out cleanly via this conceptual method: With a 5:4 ratio and three sets of 9 miles to cover, Stacy will cover 15 miles and Katie will cover 12.
Therefore, the correct answer is 15.
Alternatively, you can treat this as a problem with two variables and two solutions:
K + S = 27, and S = 5/4K
Solving for S, you’ll again find that S = 15. Press Kudos for this practice question Please help me in understanding as to where i went wrong. My approach is.. t = time taken D = total distance D s = distance covered by Stacy in time "t" D k = distance covered by Katie in time "t" S s = Speed of Stacy. S k = Speed of Katie. t = D s/S s = D k/S kt = [D-D k]/[(5/4)S k = D k/S kt = 4[27-D k]/5S k = D k/S k108 = 5D kBut answer that i got is wrong First of all, this is the way I solved this problem (using RTD chart) Let's assign some variables for the problem. X= Rate of Katie 1.25 X = Rate of Stacy (The problem says Stacy's rate is 25% faster than Katie's) I prefer using decimals and assign common variables such as X, Y not to get confuse later on. T= Time of both persons as we know they started walking at the same time. D= Distance of Katie 27-D= Distance of Stacy R T DK X T D S 1.25X T 27-D So, X.T = D and 1.25X . T = 27-D Let's put isolate D, D= 27 - 1.25X.T X.T = 27- 1.25XT 2.25XT = 27 X.T = 12 but we also know that X.T = D The distance Katie walked is 12 and thus, Stacy's distance is 27-12= 15 You made a mistake at this point: t = 4[27-D k]/5S k = D k/S kWhen multiplying (27-Dk) by 4, the term 4Dk got lost somehow  Using you variables, 4(27-Dk) / 5Sk = Dk / Sk (108 - 4Dk). Sk = 5Sk. Dk (Cross-multiplication) 108-4Dk = 5Dk 108 = 9Dk Dk= 12 Ds = 27-Dk Ds= 27-12= 15
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
14 Oct 2012, 21:28
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Their speed are in the ration 1.25 : 1. So distance travelled when they meet should also be in the same ratio. So, ((1.25)/(1.25 + 1))*27 = 15
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
15 Oct 2012, 17:01
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Solving Duration : 30 secs Solving Method : Substitute Assumption Explanation:Assume: Speed of Kat = x Speed of Stacy = 1.25x (since its 25% more than speed of Kat) Given : Distance d = 27 miles Meeting time = 27 / (x + 1.25x) => 27 / 2.25x Now, assume the least value for x which when multiplied with 2.25 would make it a whole number. Assuming x = 4, [since x = 4, speed of stacy would be 1.25x = 5] Meeting time = 27/(2.25*9) = 3 mins So at 3rd minute, distance traveled by Stacy = 5 * 3 = 15 -> Option C Answer : C. 15
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
30 Oct 2012, 22:00
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Assume the speed of katie is 6.
So the speed of Stacy will be 6(1+25/100) = 7.5
Using the formula rate x time = distance
For Stacy 7.5 x 3.6 = 27
For Katie 6 x 4.5 = 27
As it is a meeting problem we need to add Stacy's and Katie's speed.
So 7.5 + 6 = 13.5
Then Divide the distance by total rate
27/13.5 = 2
Now multiply the new time with Stacy's speed 7.5 x 2 = 15 (that is the distance Stacy would have walked when they cross each other)
Option C
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
20 Feb 2013, 20:58
I did like this:
Distance travelled by Stacy x = 125 (27-x) / 100.... Solving the equation, we get x = 15.
How did I got the values. ??
Time taken by Stacy = Time taken by Katie
Distance travelled by Stacy = x ; distance travelled by Katie = (27-x)
Speed of Stacy = 125 ; Speed of Katie = 100 (This assumption is made)
So, x/125 = (27-x)/100..... solve & we get answer = 15
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Re: Stacy and Katie plan to walk the 27-mile scenic route across
[#permalink]
20 Feb 2013, 20:58
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