Question

Roohi travels 300 km to her home partly by train and partly by bus. She takes 4
hours if she travels 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 the bus separately.​

Answer 1

Step-by-step explanation:

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.

Answer 2

Given:-

• Roohi travels 300 km to home by train and partly by bus in takes 4 hr. and travels 60 km by train and the bus in travels 100 km.

To find:-

• Find the speed of the train and the bus separately.

Solutions:-

• Let the Speed of train be y and the speed of bus be x.

Total times => 4 hours

=> 4 × 60

=> 240 mins

Now,

=> 60/y + 240/x = 240

=> (60x + 240y)/xy = 240

=> 60x + 240y = 240xy

=> 60(x + 4y) = 240xy

=> x + 4y = 240xy/60

=> x + 4y = 4xy ............(i).

=> 100/y + 200/x = 250

=> (100x + 200y)/xy = 250

=> 100x + 200y = 250xy

=> 50(2x + 4y) = 250xy

=> 2x + 4y = 250xy/50

=> 2x + 4y = 5xy ............(ii).

Subtracting Eq. (ii) and (i) we get,

${2x} \: + \: {4y} \: \: = \: \: {5xy} \\ {x} \: + \: {4y} \: \: = \: \: {4xy} \\ \underline{ \: \: \: - \: \: \: \: \: \: \: - \: \: \: \: \: \: = \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: } \\ \: {x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: {xy}$

=> y = 1

Now, putting the value of y in Eq. (i).

=> x + 4y = 4xy

=> x + 4 × 1 = 4 × x × 1

=> x + 4 = 4x

=> 4 = 4x - x

=> 4 = 3x

=> x = 4/3

Thus, Speed of bus (x) = 4/3 × 60

=> 4 × 20

=> 80 km/hr.

Speed of train (y) = 1 × 60

=> 60 km/hr.

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