Question

A train which travels at a uniform speed due to some mechanical fault after travelling for an hour goes at $3/4$ th of the original speed and reached the destination $2$ hours late. If the fault has occurred after travelling another $50$ miles, the train would have reached $40$ minutes earlier. What is the distance between the two stations?

Answer 1

Let Distance be $D$ and Velocity be $V$

$\frac{D}{V}$ is the time taken by train without Mechanical fault

Now,

$\Rightarrow (1+\frac{D-V}{\frac{3V}{4}})-\frac{D}{V}=2$

$\Rightarrow D=7V$

and when fault has occurred after travelling another 50 miles,

$\Rightarrow (1+\frac{D-V-50}{\frac{3V}{4}})-\frac{D}{V}=\frac{8}{6}$

$\Rightarrow 1200=6D-30V$

$V=100mph,D=700miles$