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On her annual road trip to visit her family in Seal Beach, California,

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Bunuel
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On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 12:22
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On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?

(A) 250
(B) 300
(C) 350
(D) 400
(E) 550

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D
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BassanioGratiano
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 15:00
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Bunuel wrote:
On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?

(A) 250
(B) 300
(C) 350
(D) 400
(E) 550

Kudos for a correct solution.


Traci ran 1/3 of the total distance.

|----------------|-------------------------------------|
1/3 traveled 2/3 has not traveled

Traci then traveled 1/4 of the remaining distance meaning there is (3/4)(2/3)X left, X representing the distance of the total trip. If this equation equals 200 miles...

(3/4)(2/3)X = 200 miles
X/2 = 200
X=400

Answer is D.
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 15:58
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Say Total Duistance =x
she traveled x/3 distance and took rest
remanining distance= x-x/3=2/3x
again, she travelled 1/4th of 2/3x distance = 2/3x*1/4=x/6

so, x/3+x/6+200=x

by solving we get, x/2=200
=> x=400

Answer is D
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 18:57
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Answer is D - 400

She travel 1/3 before stopping - 1-1/3 = 2/3 remaining
then she traveled 1/4 of the rest of the 2/3 - 2/3*1/4 = 2/12

2/3 - 2/12 = 8/12-2/12 = 6/12 = 1/2

1-1/2 = distance travel thus far and distance left.

1/2x=200
x = 400 or D
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 20:13
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I too get 400 or D.

Total distance can be written as X = X/4 + (2/3 X)(1/4) + 200.
Solving for X gives X = 400.


Bunuel wrote:
On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?

(A) 250
(B) 300
(C) 350
(D) 400
(E) 550

Kudos for a correct solution.
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 20:37
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PROBLEM:
On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?

(A) 250
(B) 300
(C) 350
(D) 400
(E) 550

SOLUTION:

Let D = total distance
Traci traveled 1/3 = D/3
i.e. remaining distance = 2D/3

She traveled 1/4 th of 2D/3 = D/6

Thus:

D = (D/3) + (D/6) + 200
D = 400

ANSWER: D
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 23:13
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Here we go -

Let the total distance = d

According to the question

d - d/3 - 1/4(d - d/3) = 200

d - d/3 - 1/4 * ( 2d/3) = 200

d -d/3 - d/6 = 200

Solving -

d/2 = 200
d = 400

Option D.
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   12 Jan 2015, 11:15
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Lets take the total distance as x miles.

1. drove (1/3)total distance = (1/3)x with (2/3)x remaining.
2. drove (1/4)remaining distance = (1/4)(2/3)x = (1/6)x
3. drove 200 miles further to destination

therefore (1/3)x + (1/6)x + 200 = x

giving x =400 miles

Ans - D
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   14 Jan 2015, 02:17
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Answer = (D) 400

Refer diagram below:

Attachment:
tot.png
tot.png [ 5.41 KiB | Viewed 3796 times ]


Let the total distance = x

First break at \(\frac{x}{3}\),

remaining distance \(= x - \frac{x}{3} = \frac{2x}{3}\)

Second break at \(\frac{2x}{3} * \frac{1}{4} = \frac{x}{6}\),

remaining distance \(= \frac{2x}{3} * (1-\frac{1}{4}) = \frac{2x}{3} * \frac{3}{4} = \frac{x}{2}\)

Given that the remaining distance \(\frac{x}{2} = 200\)

x = 400
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 19:51
Why isn't it 2/3-1/4?
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   11 Jan 2015, 20:15
bankerboy30 wrote:
Why isn't it 2/3-1/4?


Because it is 1/4th of remaining distance. Remaining distance is 2/3*total. So second leg is 1/4*2/3*Total.
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   18 Apr 2017, 00:26
Option D

Total distance = D miles
Distance traveled from Origin till First stop = 1/3rd of D

Distance traveled from First stop to second stop = 1/4th of 2/3rd of D

Remaining distance = 3/4th of 2/3rd of D = 200 miles
: (3/4)*(2/3)*D = 200 miles
: D = 400 miles
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink] New post   02 Sep 2023, 10:24
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Re: On her annual road trip to visit her family in Seal Beach, California, [#permalink]
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