Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
A) 20
B) 25
C) 28
D) 30
E) 35
OA:E
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Bill spends two days driving from Point A to Point B.
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Jay@ManhattanReview
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Hi NandishSS,NandishSS wrote:Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
A) 20
B) 25
C) 28
D) 30
E) 35
OA:E
Since Bill drove for a total of 18 hrs, with 2 hours more in the first day than the second day, he drove 10 hrs on the first day and 8 hours on the second day.
Say, the speed on the second day was x miles per hours, thus, the speed on the first day was (x + 5) miles per hours
Thus, Distance on the first day + Distance on the first day = 680
=> 10*(x + 5) + 8*x = 680
=> 10x+50+8x=680
=> 18x=630
=> x = 35 miles per hour
The correct answer: E
Hope this helps!
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Hi NandishSS,
You would likely find it easiest to create a 'data table' to keep track of this question - since the algebra behind this prompt is rather straight-forward.
Distance = (Rate)(Time)
Day 1: ____ = (R+5)(T+2)
Day 2: ____ = (R)(T)
Total Distance = 680 miles and Total Time = 18 hours....
Total time = 18 = (T+2) + T =
18 = 2T + 2
16 = 2T
8 = T
Now we know that Bill spent 10 hours on Day 1 and 8 hours on Day 2...
Day 1: ____ = (R+5)(10)
Day 2: ____ = (R(8)
We can now refer to Distance on each day in terms of R....
Day 1 distance = 10R+50
Day 2 distance = 8R
Total Distance = 680 = (10R+50) + 8R =
680 = 18R + 50
630 = 18R
35 = R
The question asks for the average speed on Day 2...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
You would likely find it easiest to create a 'data table' to keep track of this question - since the algebra behind this prompt is rather straight-forward.
Distance = (Rate)(Time)
Day 1: ____ = (R+5)(T+2)
Day 2: ____ = (R)(T)
Total Distance = 680 miles and Total Time = 18 hours....
Total time = 18 = (T+2) + T =
18 = 2T + 2
16 = 2T
8 = T
Now we know that Bill spent 10 hours on Day 1 and 8 hours on Day 2...
Day 1: ____ = (R+5)(10)
Day 2: ____ = (R(8)
We can now refer to Distance on each day in terms of R....
Day 1 distance = 10R+50
Day 2 distance = 8R
Total Distance = 680 = (10R+50) + 8R =
680 = 18R + 50
630 = 18R
35 = R
The question asks for the average speed on Day 2...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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Brent@GMATPrepNow
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First recognize that we have TWO pieces of information regarding the time Bill spent driving each day.NandishSS wrote:Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
A) 20
B) 25
C) 28
D) 30
E) 35
OA:E
On day 1, Bill drove 2 hours longer than he drove on day 2.
So, let x = # of driving hours on day 2
Then x + 2 = # of driving hours on day 1
Bill drove a TOTAL of 18 hours
So, x + (x + 2) = 18
Simplify: 2x + 2 = 18
Solve, x = 8
So, Bill drove 10 hours on day 1 and he drove 8 hours on day 2
Now let's solve the question by starting with a word equation.
Let x = speed driven on day 2
So, x + 5 = speed driven on day 1
(Distance traveled on day 1) + (Distance traveled on day 2) = 680
Distance = (rate)(time)
We get: (x+ 5)(10) + (x)(8) = 680
Expand: 10x + 50 + 8x = 680
Simplify: 18x + 50 = 680
18x = 630
x = 35 (mph)
Answer: E
Cheers,
Brent
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A shortcut. The average speed for the entire trip is 680/18 = 37 7/9mph. So this average has to fall between the speeds of the second day and the first day, right? Well, if you tested D, and the speed on the slower day was 30, the speed on the faster day would be 35, so there's no way you could get an overall average speed of over 37. If D is too small, the answer has to be E.NandishSS wrote:Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
A) 20
B) 25
C) 28
D) 30
E) 35
OA:E
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Since the total time = 18 hours, and the time on the first day is 2 hours longer than the time on the second day, the first day = 10 hours and the second day = 8 hours.NandishSS wrote:Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
A) 20
B) 25
C) 28
D) 30
E) 35
An alternate approach is to PLUG IN THE ANSWERS, which represent the speed on the second day.
When the correct answer choice is plugged in, the total distance traveled = 680 miles.
Answer choice D: 30mph per hour on the second day, implying 35mph on the first day
Since the speed on the first day = 35mph, and the time on the first day = 10 hours, the distance on the first day = rt = 35*10 = 350 miles.
Since the speed on the second day = 30mph, and the time on the second day = 8 hours, the distance on the second day = rt = 30*8 = 240 miles.
Total distance = 350+240 = 590 miles.
The total distance is TOO SMALL.
Since the total distance must INCREASE, the two speeds must also increase.
The correct answer is E.
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We are given that on the first day, Bill drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. We can let the rate on the second day = r and the rate on the first day = r + 5. Also, we can let the time on the second day = t and the time on the first day = t + 2.NandishSS wrote:Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
A) 20
B) 25
C) 28
D) 30
E) 35
Since the total time is 18, we can create the following equation to determine t:
t + t + 2 = 18
2t = 16
t = 8
Thus, the distance on day 2 is 8r and the distance on day 1 is (r + 5)(10) = 10r + 50
We can create the following equation to determine r:
8r + 10r + 50 = 680
18r = 630
r = 35
Answer: E
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