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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 26 Apr 2017, 08:17
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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 9 hours 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 26 Apr 2017, 10:42
Let distance travelled during the First Part = F
Let distance travelled during the Second Part = S

F+S = 480 --- (i)

Time Taken to complete First Part = F/55
Time Taken to complete Second Part = S/63

Total Time Taken excluding the hour-long lunch break = F/55 + S/63 = 9-1 = 8

(63F+55S)/55*63 = 8

63F+55S = 27720 --- (ii)

55F+55S = 26400
63F+55S = 27720

8F = 1320
F = 165

The amount of time spent driving before the lunch break = 165/55 = 3 hours

Answer is B. 3
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A certain road trip was completed in two parts interrupted by an hour-  [#permalink]

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New post 26 Apr 2017, 11:48
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Bunuel 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 9 hours 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 d=pre-break distance
d/55+(480-d)/63=8 hours
d=165 miles
165 miles/55 mph=3 hours
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 26 Jul 2018, 22:27
1
The trip actually took 8 hours of driving time excluding the one hour break.

Let x and y be the number of hours when the average speeds were 55 miles per hour and 63 miles per hour.
Hence,
Using Distance = Speed x Time, we can write :
x + y = 8
and
55x + 63y = 480 (Total Distance travelled)
Solving these equations gives the value of x to be 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 26 Jul 2018, 23:24
1
I did this by weighted average method.

total distance = 480
total time taken =8
average speed = 480/8 =60

by allegation method;
55 63
\ /
60
/ \
3 5

The ratio I get is part 1: part2 = 3:5

I split the total time like wise =3/8 * 8 hrs = 3 hrs.

hit kudos if that helped.
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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 27 Jul 2018, 00:31
Bunuel 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 9 hours 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


Guys, I got an interesting solution, I solved it in under 30 seconds. Just by looking at the speeds and the total distance.
Given Speed 1 = 55 mph & Speed 2 = 63 mph
The options given are all whole numbers, so 55*x + 63*y = 480 miles. We need to find "x"
In order for x to be whole number, y can be only 5 because its the only number between 1 and 9 which gives possible multiple of 55.
So then if y=5, then x=9-5-1=3
So, B is the answer in 30 sec
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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 27 Jul 2018, 01:09
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Attachment:
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Q.png [ 11.25 KiB | Viewed 167 times ]
I chose a different way to do this question because the normal way required some time consuming calculations.

I used the options to find the answer

Average speed of first half 55, and average speed of second half 63.
Total distance is 480 (units digit is 0)

Units digit of 55*option + 63*(8 - option) should be 0. (because D = S*T)
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Re: A certain road trip was completed in two parts interrupted by an hour- &nbs [#permalink] 27 Jul 2018, 01:09
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