Question

roohi travels 300 kilometre to her home partly by train and partly by bus she takes 4 hour if she travels 60 kilometre by train and remaining by bus she takes 10 minute longer find the speed of the train and that of the bus separately
guys plz help me out ​

Answer 1

Answer: Speed of train = 60 km/h  

Speed of bus = 80 km/h.

Step-by-step explanation:

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

   

According to the Question,                  

60/u + 240/v = 4 ... (i)                  

100/u + 200/v = 25/6 ... (ii)                  

Putting 1/u = p and 1/v = q in the equations, we get                  

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

⇒ 100p + 200q = 25/6                  

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

Multiplying equation (iii) by 10, we get                  

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

Subtracting equation (iv) from (v), we get 1200q = 15                  

⇒ q = 15/200 = 1/80 ... (vi)                  

Putting equation (iii), we get                  

⇒ 60p + 3 = 4                  

⇒ 60p = 1                  

⇒ p = 1/60                  

⇒ p = 1/u = 1/60 and q = 1/v = 1/80                  

⇒ u = 60 and v = 80    

           

Speed of train = 60 km/h  

Speed of bus = 80 km/h.

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Answer 2

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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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