• question_answer Directions From the four answers given, shade the appropriate answer in the space provided for it on the OW Answer Sheet. A person takes 3 h to walk a certain distance and riding back. He could walk both ways in 5 h. How long could it take to ride both ways. A) 1.5h                            B) 1h     C) 0.5h                            D) 2 h

Ans.     Suppose that person can walk at x km/h and he can ride at$y$. So, the average speed $=\frac{2xy}{x+y}km/h$ Suppose the total distance is A Now, he is only walking. So, average speed $=x\,km/h$ Total time $=\frac{2A}{x}$ $\Rightarrow$            $=\frac{2A}{x}\,\,5h$ $\Rightarrow$            $A\,\,2.5x\,km$ Now, when he is going on walk and riding back. Then, total time $\frac{\text{Distance}}{\text{Speed}}$walking time + riding time = 3 $\Rightarrow$            $\frac{2.5}{x}+\frac{2.5x}{y}=3$ $\Rightarrow$            $2.5+\frac{2.5x}{y}=3$ $\Rightarrow$            $\frac{2.5x}{y}=0.5$ $\Rightarrow$            $\frac{x}{y}=\frac{0.5}{2.5}$ $\Rightarrow$            $\frac{x}{y}=\frac{1}{5}$ or         $y=5x$ So, riding is 5 times farther then walking and it requires 5 times lesser time than walking. As it requires 5 h to walk both side. So, it requires 1 h to ride both side.