Question

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

Answer 1

Total distance travelled be Roohi=300
Let speed of train be x
Let speed of bus bus be y
Travelling 60km by train and rest by bus she took 4 hours to cover 300km
Travelling 100km by train and rest by train she took 4 hours and 10 minutes.
Putting this relations into eqn, we get,
60/x+240/y=300
100/x+200/y=300
Rearranging the above eqns 
60y+240x=300xy→(1)
100y+200x=300xy→(2)
Divide first eqn by 60
y+4x=5xy→(3)
Divide second by 50
2y+4x=6xy→(4)
Subtracting (3) from (4)
2y+4x=6xy
-y-4x=-5xy
Gives x=1km/min
=60km/hr
From eqn 

60/x+240/y=4
60/60+240/y=4
240/y=4-1
240/3=y
y=80km/hr
Speed of train is 60km/hr 
Speed of bus is 80km/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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