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Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
13 Oct 2012, 07:27
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A
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Difficulty:
45% (medium)
Question Stats:
69% (02:38) correct
31% (02:13) wrong based on 319 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?
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:
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
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?
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:
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
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
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?
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:
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
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
14 Oct 2012, 20:28
11
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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]
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
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
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 _________________
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
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]
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
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
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?
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:
Re: Stacy and Katie plan to walk the 27-mile scenic route across [#permalink]
31 Aug 2015, 03:16
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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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Expert's post
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?
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:
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.
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