Question

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes.But,if he travels 260 km by train and 240 km by taxi,he takes 6 minutes longer.Find the speed of the train and that of the taxi.

Answer 1

Let the speed of the train and taxi be x km/hr and y km/hr respectively.

Now,

time taken by train to cover 300 km $=\frac{300}{x}$ hours

and time taken by taxi to cover 200 km $=\frac{200}{y}$ hours

also

total time taken = 5 hours 30 minutes $=5\frac{1}{2}hours=\frac{11}{2}hours\Rightarrow \frac{300}{x}+\frac{200}{y}=\frac{11}{2}\Rightarrow \frac{600}{x}+\frac{400}{y}=11----\left(1\right)$

also, time taken by train to cover 260 km $=\frac{260}{x}$ hours

time taken by taxi to cover 240 km $=\frac{240}{y}$ hours

and total time taken = 5 hours 30 minutes + 6 minutes

= 5 hours 36 minutes $=5\frac{5}{3}hours=\frac{28}{5}$

$\Rightarrow \frac{260}{x}+\frac{240}{y}=\frac{28}{5}\Rightarrow \frac{325}{x}+\frac{300}{y}=7---\left(2\right)$

Putting $\frac{1}{x}=u$ and $\frac{1}{y}=v$ in (1) and (2) we get

$600u+400v=11----\left(3\right)325u+300v=7----\left(4\right)$

Solving (3) and (4)

$u=\frac{1}{100}v=\frac{1}{80}$

⇒ x = 100 and y = 80

Hence the speed of the train is 100 km/hr

and the speed of the taxi is 80 km/hr