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

Question

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

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

quantumliner · Answer

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

gracie · Answer

let d=pre-break distance
d/55+(480-d)/63=8 hours
d=165 miles
165 miles/55 mph=3 hours
B

Mayankshah · Answer

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 
55 x  + 63 y  = 480 (Total Distance travelled)
Solving these equations gives the value of  x  to be 3 hours.

Gagoosh · Answer

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.

praveenkuragodi · Answer

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

vaibhav1221 · Answer

Q.png 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 )

jalice · Answer

Average speed before lunch-break=55 mph
Average speed after lunch-break=63 mph

Lunch break= 1hr 
So, actual time taken for the trip= 9-1= 8 hr

Let time taken before lunch-break=x
Let time taken before lunch-break=8-x

So total distance: 55x+63(8-x)=480, x=3 hrs.

Ans(B)

bumpbot · Answer

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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-

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