Question

Mansi travel 300 kms to her native partly by train by bus , she takes 4hour A she travel 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 separatly .​

Answer 1

CORRECT QUESTION :-

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

SOLUTION :-

Let,

Speed of train = x

Speed of bus = y

CASE 1 :-

Distance travelled by train = 60 km

Distance travelled by bus = 240 km

Total time taken =  4 hours

$\longrightarrow\sf \dfrac{60}{x}+\dfrac{240}{y}=4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(1)$

CASE 2 :-

Distance travelled by train = 100 km

Distance travelled by bus = 200 km

$\longrightarrow \sf\dfrac{100}{x}+\dfrac{200}{x}=4+\dfrac{10}{60} \\\\\longrightarrow \dfrac{100}{x}+\dfrac{200}{x} = \dfrac{25}{6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

Let,

$\sf\dfrac{1}{x}= a \\\\\dfrac{1}{y}= b$

$\longrightarrow\sf 60a+240b = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(1) \\\\\longrightarrow 100a+200b = \dfrac{25}{6} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(2)$

Equation (1) × 5,

$\longrightarrow \sf 300a+1200b = 20 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(3)$

Equation (2) × 6,

$\longrightarrow \sf 600a+1200b = 25 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(4)$

Equation (4) - Equation (3),

$\longrightarrow\sf 300a= 5\\\\\longrightarrow a=\dfrac{5}{300}\\\\\longrightarrow \bf a =\dfrac{1}{60}$

Substitute the value of a in equation (1),

$\longrightarrow\sf 60\times \dfrac{1}{60}+240b = 4 \\\\\longrightarrow 1+ 240b = 4 \\\\\longrightarrow b =\dfrac{3}{240}\\\\\longrightarrow \bf b = \dfrac{1}{80}$

$\bullet\sf \ \dfrac{1}{x}=\dfrac{1}{60} \\\\ \ \therefore x= 60$

$\bullet\sf \dfrac{1}{y}=\dfrac{1}{80}\\\\\therefore \ y=80$

Speed of the train = 60 km/h

Speed of the bus = 80 km/h

Answer 2

$\huge\bf\purple{\mid{\fbox{\underline{\underline{Answer}}}}\mid}$

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

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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