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

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

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

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

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

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

I like the approach of substitutuion

Stacy:Katie Rate
5:4
Distance / Combined Proportional Rate * Stacy's Portion
27/9 * 5 = 15

C

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

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

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

let d=distance Stacy walks to passing
d/(27-d)=5/4
d=15 miles
C

I did it in a very simple manner:

Kate Speed = X
Stacy Speed = 5X/4

They are walking in opposite directions, so I have to sum the speeds: 9X/4

Now I apply the D = RT formula to get 27=9X/4T so time would be T=12/X

Now the last thing that I have to do is multiplying T by the Stacy Speed to get 15!

We can create the equation:

1.25rt + rt = 27

2.25rt = 27

rt = 12

So Stacy will have walked 12 x 1.25 = 15 miles when they pass each other.

Answer: C

Questions: 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?


Solution: Say Katie's speed = 4 (it makes calculation easier if you pick 4) then Stacy's speed = 1.25*4 = 5

For collision problems there is a formula
Time To meet = Gap Distance/Sum of Speeds = 27/9= 3 seconds

They took 3 seconds to meet. but the question asks Stacy's distance after 3 seconds = speed * time = 3 * 5 = 15 = C

Stacey Rate
5R/4

Katie Rate
R

When two objects converge, the distance they travel / work they perform will be equal to the distance that separated them.

Thus 5R/4 + R = 27
9R/4 = 27
9R = 108
R=12

5(12)/4 = 60/4 = 15

Thus stacey travelled 15miles