Question

A train travels 40 km at a uniform speed of $30km{h}^{-1}$. Its average speed after travelling another 40 km is $45km{h}^{-1}$ for the whole journey. Its speed in the second half of the journey is

• A. $45km{h}^{-1}$
• B. $90km{h}^{-1}$
• C. $60km{h}^{-1}$
• D. None of these

Answer 1

The correct option is B

$90km{h}^{-1}$

Let the speed of the train in later half $=x,$ then the time taken to travel later 40 km $=\frac{40}{x}$ hours
Total time taken $=\frac{40}{30}+\frac{40}{x}$
Average speed = $\frac{\text{Total distance}}{\text{Total time}}=45$
$\frac{80}{\frac{40}{30}+\frac{40}{x}}=45$
$4x+120=\frac{80}{45}\times 3x$
$x=90km{h}^{-1}$