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the sun was shining on him?

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the sun was shining on him?

by sanju09 » Thu Jun 26, 2014 2:53 am
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles per hour (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles per hour. If his average speed for the entire distance is 2.8 miles per hour, what fraction of the total distance did he cover while the sun was shining on him?
(A) 4/5
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7


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by GMATinsight » Thu Jun 26, 2014 4:01 am
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by Brent@GMATPrepNow » Thu Jun 26, 2014 6:06 am
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?

A. 1/4
B. 4/5
C. 1/5
D. 1/6
E. 1/7
Let's PLUG IN a nice value for the total distance traveled.
If Derek's average speed is 2.8 mph, then let's say that he traveled a total of 28 miles.
At an average rate of 2.8 mph, a 28 mile trip will take 10 hours.

Since Derek's average speed is BETWEEN 2 and 3 mph, we can conclude that Derek walked 2 mph when it was sunny and he walked 3 mph when it was cloudy (since his speed, in miles/hr is an INTEGER) .

Let's t = number of hours walking while sunny
So, 10 - t = number of hours walking while cloudy

We'll begin with a word equation: (distance traveled while sunny) + (distance traveled while cloudy) = 28
Since distance = (speed)(time), we can now write:
(2)(t) + (3)(10 - t) = 28
Expand: 2t + 30 - 3t = 28
Solve: t = 2
In other words, Derek walked for 2 hours while sunny.

At a walking speed of 2 mph, Derek walked for 4 miles while sunny.
So, Derek walked 4/28 of the total distance while the sun was shining on him.
4/28 = [spoiler]1/7 = E[/spoiler]

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by GMATGuruNY » Thu Jun 26, 2014 7:00 am
sanju09 wrote:On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles per hour (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles per hour. If his average speed for the entire distance is 2.8 miles per hour, what fraction of the total distance did he cover while the sun was shining on him?
(A) 4/5
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
The average speed -- 2.8 miles per hour -- must be BETWEEN the two individual rates (s and s+1).
Thus, s = 2 miles per hour and s+1 = 3 miles per hour.

We can PLUG IN THE ANSWERS, which represent the fraction traveled at 2 miles per hour.
When the correct fraction is plugged in, the average speed for the entire trip will be 2.8 miles per hour.

Answer choice D: 1/6 traveled at 2mph
Let the total distance = 6 miles.
Distance traveled at 2mph = (1/6)(6) = 1 mile, so the distance traveled at 3mph = 6-1 = 5 miles.
Total time to travel 1 mile at 2mph and 5 miles at 3mph = 1/2 + 5/3 = 13/6 hours.
Average speed for all 6 miles = (total distance)/(total time) = 6/(13/6) ≈ 2.7 miles per hour.
Eliminate D.

To INCREASE the average speed to 2.8 miles per hour, the fraction traveled at the SLOWER speed must DECREASE.
Thus, LESS than 1/6 of the total distance must be traveled at 2mph.

The correct answer is E.
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by caot » Sun Jun 29, 2014 7:22 am
A.
2.8 miles per hour
==> 2.8 * 5 <--> 5 hours (minimum integer)
==> 14

B.
x + y = 5
x * s + y(s + 1) = 14
==>s (x + y) + y = 14
==>5s + y = 14

Case 1: s = 1, then y = 9. it's impossible
case 2: s = 2. then y = 4, so x = 1

x * s / 14 = 2 / 14 = 1/7
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by knight247 » Tue Dec 02, 2014 10:48 am
Good problem.
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