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Stacy and Heather are 20 miles apart and walk towards each other along

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Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post Updated on: 24 Feb 2016, 08:07
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8
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (02:41) correct 31% (03:02) wrong based on 201 sessions

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Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?

A)7 mile
B)8 mile
C)9 mile
D)10 mile
E) 12 mile

Originally posted by Ekland on 24 Feb 2016, 08:01.
Last edited by ENGRTOMBA2018 on 24 Feb 2016, 08:07, edited 1 time in total.
Reformatted the question.
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Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post 24 Feb 2016, 08:12
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Nez wrote:
Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?

A)7 mile
B)8 mile
C)9 mile
D)10 mile
E) 12 mile


Good question to practice translation of word problems into actual equations.

Original distance between S and H = 20 miles.

Speed of S = 5+6 = 6 mph, Speed of H = 5 mph.

Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.

Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/5)+5*t=20 ---> t= 8/5 hours. Thus H has traveled for 8/5 hours giving you a total distance for H = 5*8/5 = 8 miles.

B is thus the correct answer.

Hope this helps.

P.S.: based on the wording of the question, you should calculate "how far from the original destination has Heather walked when the two meet". 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
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Re: Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post 24 Feb 2016, 10:53
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After 24 mins, Stacy travel 24/60*6=2.4m -> 6*t+5*t=20-2.4=17.6 -> t=17.6/11 -> Distance = 17.6/11*5=8
-> Answer B
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Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post 25 Feb 2016, 01:07
1
Nez wrote:
Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?

A)7 mile
B)8 mile
C)9 mile
D)10 mile
E) 12 mile


In the time, speed distance problems, it is better to write down the information first.

Attachment:
Stacy heather.JPG
Stacy heather.JPG [ 11.71 KiB | Viewed 2533 times ]


Distance traveled by Stacy in 24 minutes = 6*(24/60) = 2.4 miles

For the rest of the distance, we can use the concept of relative speed to find out after how much time will they meet
Since both are walking in the same direction, we will add the speeds.

Therefore they will meet after 17.6/11 hours = 1.6 hours
Distance travelled by Heather in 1.6 hours = 5*1.6 = 8 miles.
Option B
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Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post 25 Feb 2016, 16:46
Nez wrote:
Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?

A)7 mile
B)8 mile
C)9 mile
D)10 mile
E) 12 mile


A lot of ways to solve this problem have already been discussed. The following is my way of solving it:

Stacy
Time Speed distance
X+24 1/10(miles/min) 20-y

Heather
Time Speed distance
X 1/12(miles/min) y

Thus,

Two equations formed by Speed = Distance/time
Y=8 miles.
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Re: Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post 06 Aug 2019, 01:33
After 24 min, stancy travels 2.4

Now, distance becomes 17.6

Thus,

D=17.6/11 *5=8 m
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Re: Stacy and Heather are 20 miles apart and walk towards each other along  [#permalink]

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New post 06 Aug 2019, 11:16
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Since Stacey already covered a distance which is (6 mile/hr * 24 min) = 2.4 mile
The remaining distance is (20 - 2.4) = 17.6 mile which will be covered in 17.6 / 11(6+5) = 1.6 hr
And, in that 1.6 hr H will cover 1.6 * 5 = 8 miles.
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Re: Stacy and Heather are 20 miles apart and walk towards each other along   [#permalink] 06 Aug 2019, 11:16
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