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Jan’s house and Cindy’s house are joined by a straight road 24 miles l

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Jan’s house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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New post 27 Mar 2015, 06:00
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:54) correct 28% (02:58) wrong based on 136 sessions

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Jan’s house and Cindy’s house are joined by a straight road 24 miles long. Jan and Cindy agree to meet at a restaurant along that road, twice as far from Jan’s house as from Cindy’s. Beginning at noon, Cindy walks to the restaurant at a constant speed of 3 miles per hour. Later, Jan drives to the restaurant at a constant speed of 30 miles per hour. If they arrive at the restaurant simultaneously, at what time did Jan begin her drive?

A) 12:32
B) 1:25
C) 1:52
D) 2:08
E) 2:40

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Re: Jan’s house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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New post 27 Mar 2015, 06:21
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Since restaurant is twice as far from Jan’s house as from Cindy’s. It should be 16 miles from Jan's house and 8 miles from Cindy's.

Cindy will take 8/3 hours = 2 hours and 40 minutes to reach the restaurant.
Jan will take 16/30 hours = 32 minutes to reach the restaurant.

Hence, they Jan needs to start at 2:08 so that both reach the restaurant at same time.
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house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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New post 02 Apr 2015, 00:09
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Answer = D = 2:08

Refer diagram below:

Attachment:
rest.png
rest.png [ 4.19 KiB | Viewed 2423 times ]


Time required by Cindy \(= 60*\frac{8}{3} = 160\) minutes

Cindy reached at 14:40 to the restaurant

Time required by Jan \(= 60*\frac{16}{30} = 32\) minutes

Jan started at 14:40-0:32 = 14:08
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Re: Jan’s house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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New post 02 Apr 2015, 00:40
Bunuel wrote:
Jan’s house and Cindy’s house are joined by a straight road 24 miles long. Jan and Cindy agree to meet at a restaurant along that road, twice as far from Jan’s house as from Cindy’s. Beginning at noon, Cindy walks to the restaurant at a constant speed of 3 miles per hour. Later, Jan drives to the restaurant at a constant speed of 30 miles per hour. If they arrive at the restaurant simultaneously, at what time did Jan begin her drive?

A) 12:32
B) 1:25
C) 1:52
D) 2:08
E) 2:40


Time taken by Cindy to reach restaurant = 8/3 = 2 hour 40 mins = 160mins.
we are told Jan's speed is 10times Cindy's Speed , it means that for same distance X Jan will take 1/10 time taken by Cindy .
Since Jan has to drive for 2X distance when Cindy has to walk only for X , he will take \(\frac{2}{10}\) Time require by Cindy to walk X miles.
so Jan will take \(\frac{2}{10} * \frac{8}{3}\) = \(\frac{8}{15}\) = 32 Mins.
Jan should wait for 160-32 = 128 mins .
he should start at 2hrs 8mins past noon . i.e.\(2:08\)PM answer D
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Re: Jan’s house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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New post 02 Apr 2015, 01:44
Total Distance = 24 miles.
Let say x be the distance from Cindy’s home to Restaurant. Then distance from the Jan’s home to restaurant is 2x.
x+2x = 24
3x= 24.
X= 8.
Time taken for cindy will be approximately 8/3 hours 2.40 hours. Starting from 12 noon say more than 2. 30.
So we can eliminate answer options A, B, C and E
Because Jan will take 16/30 .. So he will take little more than 30 mins.
So the answer is D.
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Re: Jan’s house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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New post 02 Apr 2015, 06:21
Restaurant is 8 miles from Cindy's house and 16 miles from Jan's house.

So, time taken by Cindy = 8/3 hours
Time taken by Jan = 16/30 hours = 8/15 hours

So, Cindy takes (8/3 - 8/15) hours more than Jan = 8*(1/3 - 1/15) = 8*(4/15) = 128 minutes

Hence, Cindy should start 128 minutes later than Jan. So, Cindy should start 128 minutes after noon. So, Cindy should start at 2:08 pm.
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Re: Jan’s house and Cindy’s house are joined by a straight road 24 miles l  [#permalink]

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Re: Jan’s house and Cindy’s house are joined by a straight road 24 miles l   [#permalink] 03 Mar 2019, 14:31
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