Question

On a 60 km track, a train travels the first 30 km -1 with a uniform speed of 30 km h¹. How fast must the train travel the next 30 km so as to average 40 km h-¹ for the entire trip?​

Answer 1

Answer :-

Given :-

Here s₁ = s₂ = s = 30 km, v₁ = 30 km h¨¹,

v.avg = 40 km h¹, v₂ = ?

Solution :-

$v.avg \: = \frac{s₁ + s₂}{t₁ + \: t₂ }$

$v.avg \: = \frac{s + s}{ \frac{s}{v₁} + \: \frac{s}{v2} }$

$v.avg \: = \frac{2s}{ s(\frac{1}{v₁} + \: \frac{1}{v2} )}$

$v.avg \: = \frac{2v₁ \: v2}{v₁ + v2}$

$40 = \frac{2 \times 30 \times v2}{30 + v2}$

$1200 \: + 40v2 = 60 \: v2$

$20 \: v2 = 1200 = v2 = 60 \: km \:/h$

So train must travel with 60 km/h