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 \(x\) ?
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Correct Answer: Option 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}
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}