BTGModeratorVI wrote: ↑Fri Jun 05, 2020 11:40 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
Answer:
E
Source: Veritas Prep
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) =
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
= 1/7
Answer: E
Cheers,
Brent
