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Difficulty:
25%
(medium)
Question Stats:
82% (02:29) correct
18%
(02:34)
wrong
based on 251
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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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A. 2
B. 3
C. 4
D. 5
E. 6
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Let the time traveled AFTER lunch be x
Hence, the time traveled BEFORE lunch is 8-x
Given the speed before lunch is 55 miles/hr and post lunch is 63 miles/hr
55(8-x) + 63x = 480
440 - 55x + 63x = 480
440 + 8x = 480
8x = 480-440 = 40
Solving for x, x = 5
Hence the time traveled before the lunch break is 3(Option B)
Hence, the time traveled BEFORE lunch is 8-x
Given the speed before lunch is 55 miles/hr and post lunch is 63 miles/hr
55(8-x) + 63x = 480
440 - 55x + 63x = 480
440 + 8x = 480
8x = 480-440 = 40
Solving for x, x = 5
Hence the time traveled before the lunch break is 3(Option B)
General Discussion
Total average speed = 480 / 8 hours = 60 MPH
We are looking at a weighted average (by time) speed of 55 (first part of the trip) and 63 (second part of the trip)
60 falls between these 2 speeds closer to 63. Overall relationship of time is, thus, 5x to 3x
Thus, 5x + 3x = 8x and 8x = total time (8 hours) => x = 1
From our relathionship above we know that 3x corresponds to time before the lunch (we have to take less of that time - 3x and more of time after lunch - 5x to arrive to 63 mph)
Thus, time before lunch = 3. B is the answer.
We are looking at a weighted average (by time) speed of 55 (first part of the trip) and 63 (second part of the trip)
60 falls between these 2 speeds closer to 63. Overall relationship of time is, thus, 5x to 3x
Thus, 5x + 3x = 8x and 8x = total time (8 hours) => x = 1
From our relathionship above we know that 3x corresponds to time before the lunch (we have to take less of that time - 3x and more of time after lunch - 5x to arrive to 63 mph)
Thus, time before lunch = 3. B is the answer.
Attachments
q road trip.png [ 6.5 KiB | Viewed 3868 times ]
Bunuel
let d=pre-break distance
d/55+(480-d)/63=8 hours
d=165 miles
165 miles/55 mph=3 hours
B
There is an easy way to think about this problem.
Because the miles have to add up to be 480 miles, 63mph must be multiplied by a number of hours in which the units digit will equal either 5 or 0 because it has to be added to a multiple of 55mph. 5 hours is the only number to achieve that. Then don't forget the answer needs the other half! So 8-5=3 hours, thus B.
Because the miles have to add up to be 480 miles, 63mph must be multiplied by a number of hours in which the units digit will equal either 5 or 0 because it has to be added to a multiple of 55mph. 5 hours is the only number to achieve that. Then don't forget the answer needs the other half! So 8-5=3 hours, thus B.
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