Question

A train covers the first half of 80 km at a speed of 30 km/h and the second half at x km/hr. Calculate x if the average speed of the train is 45 km/h.

Answer 1

$\text{Distance covered in first half}=40km\text{Speed of the train in the first half}=30km/h\text{Then, the time taken =}\frac{40}{30}hr$

$\text{Let the speed of the train for the}\text{second half be}xkm/h.\text{Distance covered in second half}=40km\text{Then, the time taken =}\frac{40}{x}hr$

$\text{Total time taken}=(\frac{40}{30}+\frac{40}{x})\text{hr}$

$\text{Given: Average speed of whole}\text{journey}=\frac{\text{Total distance}}{\text{Total time}}=45\text{km/h}$

$\frac{80\text{km}}{\frac{40}{30}+\frac{40}{x}\text{hr}}=45\text{km/h}\frac{80}{40(\frac{1}{30}+\frac{1}{x})}=45$
$2=45\times (\frac{1}{30}+\frac{1}{x})2=(\frac{45}{30}+\frac{45}{x})2=(\frac{3}{2}+\frac{45}{x})\frac{1}{2}=\frac{45}{x}x=90\text{km/h}$