Question

A train travels some distance with a speed of 30 kilometre per hour and returns with a speed of 45 kilometre per hour calculate the average speed of the train​

Answer 1

$\sf{\underline{Solution:}}$

Let the distance covered by the train be $\boxed{\sf{\frac{x}{2}}}$

$\sf{\underline{That\:in\:the\:case\:of:}}$

Speed of 30 km/h in $\boxed{\sf{y_{1}} }$ hours.

$\sf{\underline{So:}}$

$\boxed{\sf{y_{1} = \frac{x}{2\times30}}}$

$\boxed{\sf{y_{1} = \frac{x}{60}}}$

$\sf{\underline{We\:know\:that:}}$

It covers $\boxed{\sf{ \frac{x}{2}}}$ distance,

$\sf{\underline{That\:in\:the\:case\:of:}}$

Speed of 45 km/h in $\boxed{\sf{y_{2}}}$ hours.

$\sf{\underline{So:}}$

$\boxed{\sf{y_{2} = \frac{x}{2\times45}}}$

$\boxed{\sf{y_{2} = \frac{x}{90}}}$

$\sf{\underline{Now:}}$

Total time taken is: $\boxed{\sf{(y_{1}+y_{2})}}$

$\sf{\underline{We\:know\:that:}}$

$\boxed{\sf{Average \: speed = \frac{Total \: distance}{Total \: time} }}$

$\implies$ $\sf{ \frac{x}{(y_{1} + y_{2} )}}$

$\implies$ $\sf{ \frac{1}{( \frac{1}{60} + \frac{1}{90}) }}$

$\implies$ $\sf{ \frac{1}{ \frac{(3 + 2)}{180} }}$

$\implies$ $\sf{ \frac{1}{ \frac{5}{180}} }$

$\implies$ $\sf{ \frac{180}{5}}$

$\implies$ $\boxed{\sf{ 36 \: km/h}}$

$\sf{\underline{Therefore:}}$

The average speed of the train is $\sf{36 \: km/h.}$

Answer 2

Answer:

x upon 2

Explanation: