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Anne traveled from City A to City B in 4 hours, and her speed was betw

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Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 25 Aug 2015, 23:07
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Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180


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[Reveal] Spoiler: OA

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 00:28
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For Anne:
Minimum Distance possible = Minimum Speed x Time = 25*4 = 100 miles
Maximum Distance Possible = Max. Speed x Time = 45*4 = 180 miles

For John:
Minimum Distance possible = Minimum Speed x Time = 45*2 = 90 miles
Maximum Distance Possible = Max. Speed x Time = 60*2 = 120 miles

The range for distance traveled by John & Anne between A & B is from 100 to 120 miles
Only Answer (B) - 115 Miles is in between the range.
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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 02:25
A is out since the minimum cannot be below 100.
C,D,E are out because the maximum for the second car is 120.

Thus, B.

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 02:59
Bunuel wrote:
Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180


Kudos for a correct solution.


Distance range per Anne's speed : 25*4 - 4*45 ---> 100 - 180 ...(1)

Distance range per John's speed : 45*2 - 60*2 ----> 90-120 ....(2)

(2) eliminates C,D,E and (1) eliminates A.

B is the correct answer.

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 04:04
Bunuel wrote:
Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180


Kudos for a correct solution.


Using the given options,
A.95. If distance=95 miles, and Anne takes 4 hours, then her speed=95/4=23.xx(Her speed is b/w 25 and 45 miles per hour) . So this is out
B 115. If distance=115 miles, and Anne takes 4 hours, then her speed=115/4=28.75 miles per hours(looks good) and John takes 2 hours.His speed=115/2=57.5 miles per hours(looks good)

Answer B

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 04:32
Bunuel wrote:
Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180


Kudos for a correct solution.


IMO : B

Given
25 < \(S_a\) < 45
45 < \(S_b\) < 60
\(T_a\) = 4
\(T_b\) = 2
Distance is same for both

\(S_a\)\(T_a\) = \(S_b\)\(T_b\)
\(S_a\) * 4 = \(S_b\) * 2
2* \(S_a\) = \(S_b\)

Thus from the above equation the condition is restricted to as follows
25 < \(S_a\) < 30
50 < \(S_b\) < 60
As if \(S_a\) > 30 then \(S_b\) must be >60 which is not possible

Thus sub in Distance = \(S_b\) * \(T_b\)
Distance = 2 * \(S_b\)
Thus Distance varies from
100 < Distance < 120

Thus from the options only 115 satisfies this condition
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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 07:42
Time spent by John is half the time than the time spent by Anne, as the speed of Anne is beteween the 25-45 range, John could only make the distance at a speed range from 50 to 60, if we multiply this by 2, the range of distances are from 100 to 120, so the only answer compliant with that is B

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 26 Aug 2015, 09:23
The minimum possible distance = 4*25=100 that eliminates option A
The maximum possible Distance =2*60=120 which eliminates C , D and E
thus we are then left with : B

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 24 Jan 2016, 08:04
the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180


Distance range per Anne's speed : 25*4 - 4*45 ---> 100 - 180 ...(1)

Distance range per John's speed : 45*2 - 60*2 ----> 90-120 ....(2)

(2) eliminates C,D,E and (1) eliminates A.

B is the correct answer.

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 28 Jan 2016, 11:08
Excellent question. :o :) :-D

Quick Question: How do I add this question on my downloadable PDF file??? :? :?
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Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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vabhs192003 wrote:
Excellent question. :o :) :-D

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Click on "Add question to pdf question list" as marked in the attached image.

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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw [#permalink]

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New post 20 Sep 2017, 14:53
Bunuel wrote:
Anne traveled from City A to City B in 4 hours, and her speed was between 25 miles per hour and 45 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?

A. 95
B. 115
C. 125
D. 160
E. 180


Let’s use the minimum and maximum speeds.

Minimum for Anne: 25 x 4 = 100 miles

Maximum for Anne: 45 x 4 = 180 miles

Thus:

100 < d < 180

Minimum for John: 45 x 2 = 90 miles

Maximum for John: 60 x 2 = 120 miles

Thus:

90 < d < 120

Using both inequalities, we have:

100 < d < 120

Answer: B
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Re: Anne traveled from City A to City B in 4 hours, and her speed was betw   [#permalink] 20 Sep 2017, 14:53
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