Question

On a 100 km track, a train moves the first 50 km with a uniform speed of $50km{h}^{-1}$. How fast must the train travel the next 50 km so as to have average speed $60km{h}^{-1}$ for the entire trip?

Answer 1

Let required velocity be 'v'.

Average Speed $=\frac{Distanc{e}_{\left(Total\right)}}{tim{e}_{\left(Total\right)}}$

$\Rightarrow Tim{e}_{\left(Total\right)}=\frac{100}{60}=\frac{5}{3}hr$

But, Total Time = Time taken in First 50 km + Time taken in remaining 50 Km

$\Rightarrow Tim{e}_{\left(Total\right)}=\frac{50}{50}+\frac{50}{v}=\frac{5}{3}$

$\Rightarrow \frac{50}{v}=\frac{2}{3}$

$\Rightarrow v=75km/h$