# GMAT Challenge Series (700+): Q3

Question:

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

$$\text{We know that s equals 2 as s is an integer, and 2.8 must be between s and s + 1.}$$ $$\text{Let x be the percentage of time that it is sunny}$$ $$\left({3}\right) \left({1-x}\right) + \left({2}\right) \left({x}\right) = {2.8}$$ $$\left({3 - 3x}\right) + \left({2x}\right) = {2.8}$$ $${3} - {x} = {2.8}$$ $${x} = {0.2}$$  $$\text{Therefore, 20% of time it is sunny and 80% of time it is cloudy.}$$  $$\text{distance} = \text{speed} \times \text{time}$$ $$\text{total distance} = {2.8} \times \text{t} = \text{2.8t}$$ $$\text{sunny distance} = {{2} \times \text{0.2t}} = \text{0.4t}$$ $${\text{sunny distance} \over \text{total distance}} = {\text{0.4t} \over \text{2.8t}} = \frac{1}{7}$$