Question

Abdul traveled $300$ 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 train $=x$ km/h and the speed of the taxi $=y$ km/h.

Now using $time=\frac{distance}{speed}$, we get,

$\frac{300}{x}+\frac{200}{y}=\frac{11}{2}$ ...........(1) and

$\frac{260}{x}+\frac{240}{y}=5+\frac{36}{60}=5+\frac{3}{5}=\frac{28}{5}$ ..........(2)

Let, $\frac{1}{x}$ $=m$ and $\frac{1}{y}$ $=n$ then,

$600m+400n=11$ ..........(3)

$1300m+1200n=28$ .........(4)

Now, equation $\left(3\right)\times 3-$ equation $\left(4\right)\times 4$ we get,

$500m=5\Rightarrow m=\frac{1}{100}$

$\Rightarrow x=100$ km/h.

Putting the value of $m$ in equation (3) we get,

$n=\frac{5}{400}=\frac{1}{80}$

$\Rightarrow y=80$ km/h.

Speed of train =$100$ km/h.

Speed of taxi =$80$ km/h.