Had I walked 0.5 km/hr faster, I would have taken 8 minutes less to walk 2 km. What is my original speed?
2.5 km/hr
Let the original speed be \(v\) km/hr. Time taken to walk 2 km at speed \(v\) is \(\frac{2}{v}\) hours, and at speed \((v+0.5)\) km/hr it is \(\frac{2}{v+0.5}\) hours. The difference is 8 minutes, i.e. \(\frac{2}{15}\) hour.
\(\frac{2}{v} - \frac{2}{v+0.5} = \frac{2}{15} \Rightarrow \frac{1}{v} - \frac{1}{v+0.5} = \frac{1}{15}\)
\(\frac{0.5}{v(v+0.5)} = \frac{1}{15} \Rightarrow v(v+0.5) = 7.5 \Rightarrow 2v^2 + v - 15 = 0\)
Solving, \(v = \frac{-1 \pm \sqrt{1+120}}{4} = \frac{-1 \pm 11}{4}\), so \(v = 2.5\) (rejecting the negative root). Hence the original speed is 2.5 km/hr.
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