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

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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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.

[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
B

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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Sharing the approach to work backwards from the answer options in case one is not able to form an equation or come up with the direct approach.

1. We are give that the total trip was 480 miles long and took 8 hours to complete. The speed prior to the break was 55 mph and after the break was 63 mph

2. Let's solve for the correct answer choice first i.e. B
2.a. 55 mph * 3 = 165 miles
2.b. This means that (8 - 3 = 5) hours were available post lunch. 63 mph * 5 = 315 miles
2.c. 165 + 315 = 480 miles, which is inline with the information in point 1

Apply the same process to other options and you will see that the distances do not sum up to 480 miles. Let's see an example with option A i.e. 2

55 mph * 2 = 110 miles
This means that (8 - 2 = 6) hours were available post lunch. 63 mph * 6 = 378 miles
110 + 378 = 488 miles

Ans. B
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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

Assume that time spent before lunch break = t hrs and time spent post lunch be (8- t ) hrs

55 * t + 63 ( 8-t) = 480

* Or you can also plugin each answer options in the above equation and check the unit digit to reach out to the correct answer.

55t + 63 * 8 -63t = 480
63 *8 - 60*8 = 8t
3* 8 = 8 t

t = 3 hrs

Option B

Thanks,
Clifin J Francis