emmak 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/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

assign a nice value to 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 mph and 3 mph, we can conclude that Derek walked 2 mph when it was sunny, and he walked 3 mph when it was cloudy.

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) =

28Expand: 2t + 30 - 3t =

28Solve: 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 = 1/7

Answer: E

Cheers,

Brent

_________________

Brent Hanneson – Founder of gmatprepnow.com