Question

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Roohi travels 300 km to her home partly by train and partly by bus she takes 4 hours if he travels 60 km by train and remaining by bus if he travels 100 KM by train and the remaining by bus she takes 10 minutes long find the speed of the train and the bus separately ?


Cläßß => 10th

chäp => pair of linear equation into two variables


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Answer 1

Let the speed of train be a and speed of bus be b
Speed =Distance/time

Roohi travels 300km to her home partly by train and partly by bus . She takes 4 hours if she travels 60 km by train and the remaining by bus . If she travels 100 km by train and the remaining by bus,she takes 10 minute longer .

60/a+240/b=4. (1) equation

Also, 100/a+200/b=4+10/60

100/a+200/b=25/6. (2) equation

Multiplying equation 1 by 5 and equation 2 by 3 and subtracting equation 2 from equation 1

1200/b-600/b =20-25/2

b=80km/hours
Thus 60/a+3=4
a=60km/hours
Hence speed of train is 60 km/hours and bus speed is 80km/hours

Answer 2

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$\bf{https://brainly.in/question/37581179}$

Let the speed of train and bus be u km/h and v km/h respectively.

According to the question,

$\frac{60}{u} + \frac{240}{v} = 4$....(i)

$\frac{100}{u} + \frac{200}{v} = 4 + \frac{10}{60} = \frac{25}{6}$....(ii)

Let $\frac{1}{u} = p\: and \frac{1}{v} = q$

The given equations reduce to:

60p + 240q = 4 ....(iii)

100p + 200q = $\frac{25}{6}$

600p + 1200q = 25....(iv)

Multiplying equation (iii) by 10, we obtain:

600p + 2400q = 40....(v)

Subtracting equation (iv) from equation (v), we obtain:

1200q = 15

q = $\frac{15}{1200} = \frac{1}{80}$

Substituting the value of q in equation (iii), we obtain:

60p + 3 = 4

60p = 1

p = $\frac{1}{60}$

:. p = $\frac{1}{u} = \frac{1}{60}$, q = $\frac{1}{v} = \frac{1}{80}$

u = 60 km/h , v = 80 km/h

Thus, the speed of train and the speed of bus are 60 km/h and 80 km/h respectively.

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