Roohi travels 300 km to her …

Let the speed of train =x km/h and let the speed of bus =y km/h
According to given conditions,
{tex}\frac{{60}}{x} + \frac{{240}}{y} = 4\,{\text{and}}\,\frac{{100}}{x} + \frac{{200}}{y} = 4 + \frac{{10}}{{60}}{/tex}
Let {tex}\frac{1}{x} = p\,{\text{and}}\,\frac{1}{y} = q{/tex}
Putting this in the above equations, we get
60p +240q =4 ........................... (1)
And100p +200q = {tex}\frac{{25}}{6}{/tex} ............................. (2)
Multiplying (1) by 5 and (2) by 3, we get
300p +1200q = 20 ......................... (3)
300p +600q = {tex}\frac{{25}}{2}{/tex}......................... (4)
Subtracting (4) from (3), we get
600q =20− {tex}\frac{{25}}{2}{/tex} =7.5 ⇒ q = {tex}\frac{{7.5}}{{600}}{/tex}
Putting value of q in (2), we get
100p +200{tex}\left( {\frac{{7.5}}{{600}}} \right) = \frac{{25}}{6}{/tex}
⇒ 100p + 2.5 = {tex}\frac{{25}}{6}{/tex}
⇒ 100p = {tex}\frac{{25}}{6}{/tex} - 2.5
⇒ p = {tex}\frac{{10}}{{600}}{/tex}
But {tex}\frac{1}{x} = p\;{\text{and}}\;\frac{1}{y} = q{/tex}
Therefore, x = {tex}\frac{{600}}{{10}} = 60{/tex} km/h and y = {tex}\frac{{600}}{{7.5}}{/tex} = 80km/h
Therefore, speed of train =60 km/h
And, speed of bus =80 km/h