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

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Re: Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
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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]
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]
8/35 - 8/55 ~= 5

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Re: Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
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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]
=>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]
2
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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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Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
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

PS21149

Because we're trying to find the difference in approximate minutes it would take with the new vs old speed, we can use estimation
We are trying to find New Time - Old Time = X

Since we're dealing with Rates and Distance; Use the formula Rate * Time = Distance

Old speed limit: 55 mph * T1 = 8

T1 = $$\frac{8}{55} * 60$$ minutes, we need to multiply by 60 to get it in mins

T1 $$\frac{480}{55}$$ minutes

New speed limit: 35 mph * T1 = 8

T2 = $$\frac{8}{35} * 60$$ minutes, we need to multiply by 60 to get it in mins

T2 $$\frac{480}{35}$$ minutes

This is where estimation comes in handy:

T1 $$\frac{480}{55}$$ minutes, we know that 55*10 = 550 mins, and 55*9 = 495. So T1 is approx 9 mins

T2 $$\frac{480}{35}$$ minutes, we know that 35*10 = 350. You can subtract 480 - 350 = 130. 35 can go into 130 around 4 times (35*4 = 140). So 10 + 4 = approx 14 mins

~14 - ~9 = Approx 5

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Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
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distance = rate * time

distance/rate = time

$$\frac{8}{55} * 60 = \frac{96}{11} = 9$$ minutes

$$\frac{8}{35} = \frac{96}{7} = 14$$ minutes

$$14 - 9 = 5$$ minutes

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Re: Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
Given: 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.
Asked: 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 ?

Change in time required to travel along the section of highway = (8/35 - 8/55)*60 = (8/7 - 8/11)*12 = (11-7)8*12/77 = 4*8*12/7*11 ~ 5 minutes

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

55 mph is almost 1 mile/minute. So at that speed, the trip takes just over 8 minutes. 35 mph is more than half the original speed, so a trip at that speed will take less than double the original time. That means the increase is less than 8 minutes, so A.
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Re: Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
Since the fractions are a bit tedious, I made one assumption.

- Let the distance be 80 miles instead of 8 miles.

Case 1 = @55 mph
Time = 80/55 gives 1.4 hours & for 8 miles we shift a decimal 0.14 hours

Case 2 = 35 mph
Time = 35/55 gives 2.2 hours & for 8 miles we shift a decimal 0.22 hours

Here the difference in 0.22 & 0.14 hours gives the time saved (i,e, 0.08 hours)
0.08 hours is nothing but 8% of 60 minutes and basically any number less than 10% i.e 6 minutes.

Hence answer is A = 5 minutes.
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Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
­Classic distance problem- subtract the times:

­
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Re: Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
why cant i do this by stating that since cars are going 20 mph Slower that means 8/20 is the time in hours that was slowed down…?
Re: Due to construction, the speed limit along an 8-mile section of highwa [#permalink]
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