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Stacy and Katie plan to walk the 27-mile scenic route across

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Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 13 Oct 2012, 07:27
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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

[Reveal] Spoiler: OE
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.


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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 14 Oct 2012, 04:49
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

[Reveal] Spoiler: OE
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.


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Please help me in understanding as to where i went wrong.

My approach is..

t = time taken
D = total distance
Ds = distance covered by Stacy in time "t"
Dk = distance covered by Katie in time "t"
Ss = Speed of Stacy.
Sk = Speed of Katie.

t = Ds/Ss = Dk/Sk
t = [D-Dk]/[(5/4)Sk = Dk/Sk
t = 4[27-Dk]/5Sk = Dk/Sk
108 = 5Dk

But answer that i got is wrong :(
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 14 Oct 2012, 12:04
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

[Reveal] Spoiler: OE
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.



[Reveal] Spoiler: Liked?
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Please help me in understanding as to where i went wrong.

My approach is..

t = time taken
D = total distance
Ds = distance covered by Stacy in time "t"
Dk = distance covered by Katie in time "t"
Ss = Speed of Stacy.
Sk = Speed of Katie.

t = Ds/Ss = Dk/Sk
t = [D-Dk]/[(5/4)Sk = Dk/Sk
t = 4[27-Dk]/5Sk = Dk/Sk
108 = 5Dk

But 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 D
K 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-Dk]/5Sk = Dk/Sk

When 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] New post 14 Oct 2012, 20:28
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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] New post 15 Oct 2012, 16:01
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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] New post 30 Oct 2012, 21:00
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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] New post 20 Feb 2013, 19:58
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] New post 25 Aug 2013, 15:29
MacFauz wrote:
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



Can you please explain how you get or why you have ((1.25)/(1.25 + 1))*27 ??

Thanks
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 25 Aug 2013, 21:05
jjack0310 wrote:
MacFauz wrote:
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



Can you please explain how you get or why you have ((1.25)/(1.25 + 1))*27 ??

Thanks

Lets say a basket contains apples and oranges in the ratio 1:2

To represent this in the form of a fraction, we can say that \(\frac{1}{3}\) of the basket is apples and \(\frac{2}{3}\) of the basket is oranges. i.e. We add up the numbers and divide each number by the sum to get the corresponding fraction.

Since distances are in the ratio 1.25 (Distance travelled by Stacy):1 (Distance travelled by Katie)
So the distance travelled by Stacy will be \(\frac{1.25}{2.25}\) of the total distance

Hope it's clear
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 27 Aug 2013, 09:18
MacFauz wrote:
jjack0310 wrote:
MacFauz wrote:
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



Can you please explain how you get or why you have ((1.25)/(1.25 + 1))*27 ??

Thanks

Lets say a basket contains apples and oranges in the ratio 1:2

To represent this in the form of a fraction, we can say that \(\frac{1}{3}\) of the basket is apples and \(\frac{2}{3}\) of the basket is oranges. i.e. We add up the numbers and divide each number by the sum to get the corresponding fraction.

Since distances are in the ratio 1.25 (Distance travelled by Stacy):1 (Distance travelled by Katie)
So the distance travelled by Stacy will be \(\frac{1.25}{2.25}\) of the total distance

Hope it's clear




Adding to the same approach:
Ratio of Speeds
Stacy/Katie = 1.25/1 = 5/4
So their distance also should be in the ratio of 5/4 (as time traveled is same)
Total distance =27
Dividing it in the ratio of 5/4, we get distance traveled by stacy = 5*(27/9) = 15
So option C
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 03 Mar 2014, 18:25
I like the approach of substitutuion
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 03 Mar 2014, 19:22
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Stacy:Katie Rate
5:4
Distance / Combined Proportional Rate * Stacy's Portion
27/9 * 5 = 15

C
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 09 May 2014, 02:12
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

[Reveal] Spoiler: OE
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.


[Reveal] Spoiler: Liked?
Press Kudos for this practice question :-D




What is the need to going into deep ? I don't think there is any explicit need of
substitution or complexity to be followed.

Let Katie travelled at speed of ' x ' and distance of ' d '.

let stacy travelled at speed of ' 1.25x ' and distance of ' 27-d '

so Katie: speed=dist/time => x=d/t
so stacy: speed=dist/time=> 1.25x=27-d/t

substitute then for ' x '

1.25d/t=27-d/t

1.25d=27-d

2.25d=27

d= 2700/225

d= 12

so stacy travelled: 27-12=15
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 21 May 2014, 07:04
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Stacy and Katie will met when in equal time t total distance covered by both of them will be 27 miles.

Lets time is t and speed of Katie is v. then speed of Stacy is 1.25v

v*t + 1.25v * t = 27

2.25v*t = 27

v*t = 27/2.25 = 12

distance covered by Katie = v*t = 12

distance covered by Stacy = 27-12 = 15 miles

Hence Answer is C
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 31 Aug 2015, 03:16
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 31 Aug 2015, 20:06
5/4=d/27-d
d=15 miles
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Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink] New post 31 Aug 2015, 21:58
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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

[Reveal] Spoiler: OE
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.


[Reveal] Spoiler: Liked?
Press Kudos for this practice question :-D


This question is perfectly suited to using ratios.

Stacy's speed is 5/4 of Katie's speed. So in the same time, Stacy's distance covered will be 5/4 of Katie's distance covered. That is, they will cover distance in the ratio 5:4. Total distance on ratio scale is 5+4 = 9 but actually it is 27 so multiplication factor is 27/9 = 3.
Distance covered by Stacy = 5*3 = 15 miles.

For more on ratios, check:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
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Re: Stacy and Katie plan to walk the 27-mile scenic route across   [#permalink] 31 Aug 2015, 21:58
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