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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