Question

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

• A. $45km{h}^{-1}$
• B. $90km{h}^{-1}$
• C. $60km{h}^{-1}$
• D. $30km{h}^{-1}$

Answer 1

The correct option is B

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

In the first half, distance covered = 40 km and speed = $30km{h}^{-1}$,
then time taken to travel $=\frac{\text{distance}}{\text{speed}}=$$\frac{40}{30}$ hours.

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