Question

Mansi travels 300 kms to her native partly by train and partly by bus. She takes 4 hours, if she travels 60 kms by train and the remaining by bus. If she travels 100 kms by train and the remaining by bus, she takes 10 minutes longer. Find the average speed of the train and the bus separately.​

Answer 1

$\displaystyle\Huge \bf\red{\underline{\underline{ANSWER}}} </p><p>$

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

$\huge \boxed{\sf{Time = \frac{Distance}{speed}}} </p><p>$

Total distance =300 km

Mansi travels 60 km by train and 300−60=240 by bus in 4 minute,

$\bf\frac{60}{x} + \frac{240}{y} = \red4</p><p>$

and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,

$\bf {\frac{100}{x} + \frac{200}{y} = 4 + \frac{1}{6} = \frac{24 + 1 }{6} = \purple{\frac{25}{6}}}</p><p>$

Now, let

$\bf\color{blue}{\frac{1}{x} = a}$

and.

$\bf \color{blue}{ \frac{1}{y} = b }$

$\bfthen 60a+240b=4.............(1)$

$\bf100a+200b=25/6----(2)$

multiply (1) by 5 and (2) by 6 we get

$\bf300a+1200b=20..........(3)$

$\bf600a+1200b=25...........(4)$

Subtracting (3) and (4) we get

$\bf \green{−300a=−5}$

$\bf{a = \frac{1}{60}}$

Putting the value of a in (1) we get

$\bf{60 \times \frac{1}{60} + 240b = 4}$

$</p><p> \bf240b = 3 \\ \\ \bf b = \frac{1}{80}$

Now ,

$\bf\frac{1}{x} = a \\ \\ \bf \red{a = 60 km/h \: \blue \bigstar}$

$\bf\frac{1}{y} = b \\ \\ \bf \red {b = 80 km/h \: \pink \bigstar}$

Hence, the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.

Answer 2

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 Time=

Speed

Distance

Total distance =300 km

Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,

refer to the attachment