Question

Roohi travels 600 km to her home partly by train and partly by bus .She takes 26/3hours if travels 320km by train and the remaining by bus if she travels 200km by train and the remaining by bus she takes 55/6hours.find the speed of the train and the bus.

Answer 1

Answer:

Let the speed of the train be x km/hr and the speed of the bus is y km/hr.

So according to question and using Time=

Speed

Distance

Total distance =300 km

Roohi travels 60 km by train and 300−60=240 by bus in 4 minute,

x

60

+

y

240

=4

and 100 km by train, 300−100=200 by bus, and takes 10 minutes more,

x

100

+

y

200

=4+

60

10

⇒

x

100

+

y

200

=

6

25

Now, let

x

1

=u and

y

1

=v

then 60u+240v=4.............eq1

100u+200v=

6

25

..............eq2

multiply eq1 by 5 and eq2 by 6 we get

300u+1200v=20..........eq3

600u+1200v=25...........eq4

Subtracting eq3 qnd eq4 we get

−300u=−5

u=

300

5

=

60

1

Putting the value of u in eq1 we get

60×

60

1

+240v=4

240v=3

v=

240

3

=

80

1

Now

x

1

=u=

60

1

∴x=60

and

y

1

=v=

80

1

∴y=80

Hence the speed of the train is 60 km/hr and the speed of the bus is 80 km/hr.

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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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