Question

A person covers first one third of the journey with a speed of 10 kmph, next one third of the journey with a speed of 60 kmph and the rest with a speed of 30 kmph. Find the average speed

Answer 1

$let \: the \: total \: distance \: travelled \: \\ by \: the \: man \: be \: x \\ time \: taken \: to \: cover \: one - third \: \\ of \: the \: distance = \frac{x}{3 \times 10} = \frac{x}{30 } \: \\ time \: taken \: to \: cover \: other \: one - third \: of \: \\ the \: journey = \frac{x}{60 \times 3} = \frac{x}{180} \\ tim \: taken \: to \: cover \: remaining \: part = \frac{x}{3 \times 30} \\ total \: time \: taken = \frac{x}{30} + \frac{x}{180} + \frac{x}{90} = \frac{6x + x + 2x}{180} = \frac{x}{20} \\ total \: distance = x \\ average \: speed = \frac{total \: distance \: travelled}{total \: time \: taken} \\ average \: speed = \frac{x}{ \frac{x}{20} } = 20 \\ (hope \: it \: helps)$