A cyclist rode for 30 minutes at \(x km / hr\) and due to a breakdown. he had to push the bike for \(2 hrs\) at \((x-5) km / hr\). if the total distance covered is less than \(60 km\), what is the range of values for \(x\) ?
A. x<14 B. x<29 C. x<28 D. x<20
Correct Answer: C
Explanation
First distance \(=\) speed \(\times\) time \begin{aligned} &=x \frac{ km }{ hr } \times \frac{1}{2} hr =\frac{x}{2} km \\ \text { Second distance } &=(x-5) \times 2 \\ &=2 x-10 \\ \text { Total distance } &=2 x-10+\frac{x}{2} \\ &=\frac{5 x}{2}-10<60 \\ 5 x &<70 \times 2 \\ & \Rightarrow x<\frac{140}{5} \Rightarrow x<28 \end{aligned}
