GMAT Challenge Series (700+): Q17

Cloud Sun.jpg

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

MBA Wisdom's Answer:

$$\textit{sunny speed} = \textit{s}$$ $$\textit{cloudy speed} = \textit{s} + {1}$$ $$\textit{average speed} = {2.8} \textit{ miles/hr}$$ $$$$ $$\text{The average speed must be between } \textit{s} \text{ and } \textit{s} + {1}$$ $$\text{As } \textit{s} \text{ is an integer and the average speed is 2.8 } \textit{s} \text{ must equal 2}$$ $$\text{This implies that the ratio of time sunny:cloudy is 1:4}$$ $$$$ $$\text{Let the sunny time be: } \textit{t}$$ $$\text{Then the cloudy time will be: } {4}\textit{t}$$ $$$$ $$\textit{distance} = \left(\textit{speed}\right) \left(\textit{time}\right)$$ $$\textit{sunny distance} = {{2} \textit{t}}$$ $$\textit{cloudy distance} = {\left({3}\right) \left({4}\textit{t}\right)} = {{12} \textit{t}}$$ $$\textit{total distance} = \textit{sunny distance} + \textit{cloudy distance}$$ $$\textit{total distance} = {{{2} \textit{t}} + {{12} \textit{t}}} = {{14} \textit{t}}$$ $$$$ $${\textit{sunny distance} \over \textit{total distance}} = {{{2} \textit{t}} \over {{14} \textit{t}}} = {{1} \over {7}}$$

E. 1/7