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A certain road trip was completed in two parts interrupted by an hour-

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A certain road trip was completed in two parts interrupted by an hour-  [#permalink]

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New post 02 Feb 2017, 07:25
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A certain road trip was completed in two parts interrupted by an hour-long lunch break. During the first portion of the trip the average speed was 55 miles per hour and the average speed during the second part of the trip was 63 miles per hour. If the trip was 480 miles long and took a total of 8 hours (excluding the time stopped for lunch) then which of the following is the amount of time spent driving before the lunch break?

A) 2
B) 3
C) 4
D) 5
E) 6

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Re: A certain road trip was completed in two parts interrupted by an hour-  [#permalink]

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New post 02 Feb 2017, 07:45
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duahsolo wrote:
A certain road trip was completed in two parts interrupted by an hour-long lunch break. During the first portion of the trip the average speed was 55 miles per hour and the average speed during the second part of the trip was 63 miles per hour. If the trip was 480 miles long and took a total of 8 hours (excluding the time stopped for lunch) then which of the following is the amount of time spent driving before the lunch break?

A) 2
B) 3
C) 4
D) 5
E) 6


Average speed of entire trip = 480/8 = 60 miles/hr

Apply the allegation rule(please refer the attached diagram).

We get the ratio of time spent = 3:5. Hence time spent before lunch break = 3 hrs.
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Re: A certain road trip was completed in two parts interrupted by an hour-  [#permalink]

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New post 02 Feb 2017, 10:32
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[quote="duahsolo"]A certain road trip was completed in two parts interrupted by an hour-long lunch break. During the first portion of the trip the average speed was 55 miles per hour and the average speed during the second part of the trip was 63 miles per hour. If the trip was 480 miles long and took a total of 8 hours (excluding the time stopped for lunch) then which of the following is the amount of time spent driving before the lunch break?

A) 2
B) 3
C) 4
D) 5
E) 6[/quote

let x=time before break
y=time after break
y=8-x hours
55x+63(8-x)=480 miles
x=3 hours
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Re: A certain road trip was completed in two parts interrupted by an hour-  [#permalink]

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New post 08 Feb 2017, 11:19
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duahsolo wrote:
A certain road trip was completed in two parts interrupted by an hour-long lunch break. During the first portion of the trip the average speed was 55 miles per hour and the average speed during the second part of the trip was 63 miles per hour. If the trip was 480 miles long and took a total of 8 hours (excluding the time stopped for lunch) then which of the following is the amount of time spent driving before the lunch break?

A) 2
B) 3
C) 4
D) 5
E) 6


We are given that the average speed before lunch was 55 mph. If we let t equal the time spent traveling before lunch, the distance covered is 55t.

Since the trip takes 8 hours, excluding the lunch break, the second part of the trip takes 8 - t hours and the distance covered in this part is 63(8 - t).

Since the sum of the distances in the first and second parts must equal the total length of the trip, which is 480 miles, we can create the following equation and determine t:

55t + 63(8 - t) = 480

55t + 504 - 63t = 480

24 = 8t

t = 3

Answer: B
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Re: A certain road trip was completed in two parts interrupted by an hour-  [#permalink]

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New post 05 Mar 2018, 10:52
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duahsolo wrote:
A certain road trip was completed in two parts interrupted by an hour-long lunch break. During the first portion of the trip the average speed was 55 miles per hour and the average speed during the second part of the trip was 63 miles per hour. If the trip was 480 miles long and took a total of 8 hours (excluding the time stopped for lunch) then which of the following is the amount of time spent driving before the lunch break?

A) 2
B) 3
C) 4
D) 5
E) 6


Let's start with a word equation

(distance traveled during FIRST part of trip) + (distance traveled during SECOND part of trip) = 480 miles

Let t = time spend on FIRST part of trip (in hours)
So, 8-t = time spend on SECOND part of trip (since the ENTIRE driving time was 8 hour)

Distance = (speed)(time)

So, we can write: (55)(t ) + (63)(8 - t) = 480
Expand: 55t + (504 - 63t) = 480
Simplify: -8t + 504 = 480
Subtract 504 from both sides: -8t = -24
Solve: t = 3

Answer: B

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Re: A certain road trip was completed in two parts interrupted by an hour-   [#permalink] 05 Mar 2018, 10:52
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