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Due to construction, the speed limit along an 8-mile section of highwa

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Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 07 Apr 2011, 05:46
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  55% (hard)

Question Stats:

66% (02:32) correct 34% (02:29) wrong based on 278 sessions

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Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 24
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post Updated on: 07 Apr 2011, 06:03
Let t1 is time taken @ 55 mph
t1 = 8/55
Let t2 is time taken @ 35 mph
t2 = 8/35
Difference in time = 8/35 - 8/55 = 8 * 20 / (35 * 55) hr = 160 * 60 / (35 * 55) mins = 4.7 = 5 (approx) mins
Acer86 wrote:
Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 24

Originally posted by gmat1220 on 07 Apr 2011, 05:59.
Last edited by gmat1220 on 07 Apr 2011, 06:03, edited 1 time in total.
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 07 Apr 2011, 06:00
8/35 - 8/55 = 8/5 * ( 11 - 7)/77

= 8/5 * 4/77 * 60 min

= 8 * 12 * 4/77

= 384/77 ~ 4.9

Answer - A
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 07 Apr 2011, 06:03
Acer86 wrote:
Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 24


Old time in minutes to cross 8 miles stretch = 8*60/55 = 8*12/11 = 96/11= 8.72
New time in minutes to cross 8 miles stretch = 8*60/35 = 8*12/7 = 13.71

Time difference = 13.71-8.72= 5

Ans: "A"
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 07 Apr 2011, 06:55
I wondering if someone can use componendo / dividendo since t1/t2 is known. Hence average speed and average time can come into picture. Otherwise there is no takeaway from this problem.
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 07 Apr 2011, 16:28
8/35 - 8/55 ~= 5

Answer is A.
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 08 Apr 2011, 02:38
Acer86 wrote:
Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 24


Since answer choices are fairly dispersed, we can use approximations here.

Difference is given by \(8*60/35 - 8*60/55\)

We can substitute 36 instead of 35 and 54 instead of 55 in expression above without sacrificing accuracy too much

We will get \(8*10/6-8*10/9 = 8*10*(1/6-1/9) = 8*10/18\) ~4.5 ~5
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 08 Apr 2011, 19:00
=>55 x t1 = 35 x t2
=>t2 = 11/7 x t1
=> t2- t1 = 4/7 t1 = 4 x 8 / (7 x 55)
=> 1/16 (approx) hours
1/10 hrs is 6 mins, and 1/20 hr is 3 mins so 1/16 is around 4 and 5
Ans = A
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Re: Due to construction, the speed limit along an 8-mile section of highwa  [#permalink]

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New post 27 Jun 2018, 03:20
1
Acer86 wrote:
Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 24


Original time in minutes = \(\frac{d}{r} * 60 = \frac{8}{55} * 60 = \frac{8}{11} * 12 ≈ 9\) minutes.

\(\frac{new-speed}{original-speed} = \frac{35}{55} = \frac{7}{11}\)
Since the rate and time have a reciprocal relationship:
\(\frac{new-time}{original-time} = \frac{11}{7} ≈ \frac{3}{2}\)

The resulting time ratio indicates that the new time is about 50% greater than the original time.
Thus:
Time increase in minutes ≈ 50% of 9 = 4.5.


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Re: Due to construction, the speed limit along an 8-mile section of highwa &nbs [#permalink] 27 Jun 2018, 03:20
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