Question

roohi travels 300 km to her home partly by train and partly by bus she takes 4 hours if you travel 60 kilometre by train and the remaining by bus if you travel 100 KM by train and the remaining by bus she takes 10 minutes longer find the speed of the train and double separately​

Answer 1

Answer:

let speed of train be xkm/hr

speed of bus be ykm/hr

case:-1- 60/x+240/y=4

case:-2- 100/x+200/y=25/6

(60/x+240/y=4)×5

(100/x+200/y=25/6)×3

300/x+1200/y=20

-300/x+600/y=25/2 by elimination method

we get

600/y=15/2

y=600×2/15=80km/hr

from 1

60/x+240/y=4

60/x+3=4

x=60km/hr..

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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