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/h and y km/h respectively.
Then as per the question
$\frac{3}{x}+\frac{2}{y}=\frac{11}{200}.....\left(i\right)$
When the speeds of the train and taxi are 260 km and 240 km respectively, then
$$\begin{gathered} \frac{260}{x}+\frac{240}{y}=\frac{11}{2}+\frac{6}{60} \\ \Rightarrow \frac{13}{x}+\frac{12}{y}=\frac{28}{100}.....\left(ii\right) \end{gathered}$$
Multiplying (i) by 6 and subtracting (ii) from it, we get
$$\begin{gathered} \frac{18}{x}-\frac{13}{x}=\frac{66}{200}-\frac{28}{100} \\ \Rightarrow \frac{5}{x}=\frac{10}{200}\Rightarrow x=100 \end{gathered}$$
Putting x = 100 in (i), we have
$$\begin{gathered} \frac{3}{100}+\frac{2}{y}=\frac{11}{200} \\ \Rightarrow \frac{2}{y}=\frac{11}{200}-\frac{3}{100}=\frac{1}{40} \\ \Rightarrow y=80 \end{gathered}$$
Hence, the speed of the train and that of the taxi are 100 km/h and 80 km/h respectively.