Respuesta :
Answer:
[tex]\displaystyle\Huge \bf\red{\underline{\underline{ANSWER}}}
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Let the speed of the train be x km/hr and the speed of the bus is y km/hr.
So according to question and using
[tex] \huge \boxed{\sf{Time = \frac{Distance}{speed}}}
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Total distance =300 km
Mansi travels 60 km by train and 300−60=240 by bus in 4 minute,
[tex] \bf\frac{60}{x} + \frac{240}{y} = \red4
[/tex]
and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,
[tex] \bf {\frac{100}{x} + \frac{200}{y} = 4 + \frac{1}{6} = \frac{24 + 1 }{6} = \purple{\frac{25}{6}}}
[/tex]
Now, let
[tex]\bf\color{blue}{\frac{1}{x} = a}[/tex]
and.
[tex] \bf \color{blue}{ \frac{1}{y} = b }[/tex]
[tex]\bfthen 60a+240b=4.............(1)[/tex]
[tex]\bf100a+200b=25/6----(2)[/tex]
multiply (1) by 5 and (2) by 6 we get
[tex]\bf300a+1200b=20..........(3)[/tex]
[tex]\bf600a+1200b=25...........(4)[/tex]
Subtracting (3) and (4) we get
[tex]\bf \green{−300a=−5}[/tex]
[tex]\bf{a = \frac{1}{60}}[/tex]
Putting the value of a in (1) we get
[tex]\bf{60 \times \frac{1}{60} + 240b = 4}[/tex]
[tex]
\bf240b = 3 \\ \\ \bf b = \frac{1}{80} [/tex]
Now ,
[tex] \bf\frac{1}{x} = a \\ \\ \bf \red{a = 60 km/h \: \blue \bigstar}[/tex]
[tex] \bf\frac{1}{y} = b \\ \\ \bf \red {b = 80 km/h \: \pink \bigstar} [/tex]
Hence, the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.