Question

A train travels at the average speed of 153 km/h without including time spend of station if we include spend stations the speed drop 72km/h. how much time does the train spend at the station per hour​

Answer 1

Time the train spend at the station per hour​ is $(\frac{9}{17})$.

Explanation:

1. Here train speed without stoppage $V_{1}=153(\frac{km}{h})$.

2. Train speed with stoppage $V_{2}=72(\frac{km}{h})$.

3. Let stoppage time at stations = $\Delta t(h)$

4. Time taken during travels without stoppage = t(h)

5. So total time taken during travels with stoppage= $t+\Delta t (h)$

6. If distance travel by trains =d (km)

7. So

   Time taken during travels without stoppage$(t)=\frac{d}{V_{1}}$   ...1)

   Total time taken during travels with stoppage $(t+\Delta t)=\frac{d}{V_{2}}$      ...2)

8. Subtract equation 1) from equation 2)

   $\Delta t=\frac{d}{V_{2}}-\frac{d}{V_{1}}$

   $\Delta t=\frac{d\times (V_{1}-V_{2})}{V_{1}\times V_{2}}$     ...3)

9. Now equation 3) ÷ equation 2)

  $\frac{\Delta t}{t+\Delta t}=\frac{\frac{d\times (V_{1}-V_{2})}{V_{1}\times V_{2}}}{\frac{d}{V_{2}}}$

  So

  $\frac{\Delta t}{t+\Delta t}=\frac{(V_{1}-V_{2})}{V_{1}}$        ...4)

  Equation 4) is known as time spend at station per hour of total journey

10. So

   Time spend at station per hour of total journey = $\frac{(V_{1}-V_{2})}{V_{1}}$

   On putting the speed we get

   Time spend at station per hour of total journey = $\frac{(153-72)}{153}$

 So

  Time spend at station per hour of total journey = $\frac{9}{17}$