Question

Gaurav travels 300 km to his home partly by train and partly by bus. He takes 4 hours if he travels 60 km by train and the remaining by bus. If he travels 100km by train and the remaining by bus, he takes 10 minutes longer. Find the speed of the train and the bus separately

Answer 1

Answer :

• Speed of train = 60 km/h
• speed of Bus = 80 km/h

Explanation :

It is given that,

• Gaurav travels 300 km to his home partly by Train and partly by Bus

Let, speed of train = x and speed of Bus = y

Now,

Using formula time = distance / speed and

Considering Condition 1

• When Gaurav travels 60 km by train and remaining by Bus he takes 4 hours

so,

→ 60/x  +  ( 300 - 60 )/y = 4

→ 60/x  + 240/y = 4

[ dividing by 4 both sides ]

→ 15/x  +  60/y = 1  

→ 15/x  + 60/y = 1

→ 15/x = 1   -  60/y

→ 15/x = ( y - 60 )/y

→ 1/x = (y-60) / (15 y)  ___equation (1)

Now,

Considering condition 2

• When Gaurav travels 100 km by train and remaining by bus

he takes 10 minutes longer ( means he takes 1/6 hrs longer , so total time taken will become 25/6 hrs )

→ 100/x  +  ( 300 - 100 )/y = 25/6

→ 100/x  + 200/y = 25/6

[ dividing by 25 both sides ]

→ 4/x  +  8/y  = 1/6

→ 4(1/x)  + 8/y = 1/6

[ putting equation (1) ]

→ 4 [(y-60)/(15y) ] + 8/y = 1/6

→ (4 y - 240)/(15 y)  +  8/y = 1/6

→ ( 4 y - 240 + 120 )/( 15 y ) = 1/6

→ 4 y - 120 = 15 y / 6

→ 24 y - 720 = 15 y

→ 9 y = 720

→ y = 80

[ putting value of y in equation (1) ]

→ 1/x = ( y - 60 ) / ( 15 y )

→ 1/x = ( 80 - 60 ) / ( 15 × 80 )

→ 1/x = 20 / ( 15 × 80 )

→ x = 60

therefore,

• speed of train is 60 km/h
• speed of Bus is 80 km/h.

Answer 2

$\bf\large{\underline{Solution:-}}$

• Let the speed of train be x km/h.
• And the speed of bus be y km/h

we know,

→Time = Distance/speed

Guvrav travel 60km by train

so,

→300 - 60 = 240km by bus in 4 minute

→60/x + 240/y = 4

• And km by train , 300 - 109 = 200 by bus

and takes 10 minutes more,

→100/x + 200/y = 4 + 10/60

→ 100/x + 200/y = 25/6

Now,.

let 1/x = u and 1/y = v

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

→ 100u + 200v = 6/25 ..............eq2

• multiply eq1 by 5 and eq2 by 6 we get

→ 300u + 1200v = 20-----equ(3)

→ 600u + 1200v = 25----equ(4)

• Subtracting eq3 qnd eq4 we get

→ -300u = −5

→ u = 5/300

→ u = 1/60

• Putting the value of u in eq1 we get

→ 60 × 1/60 + 240v = 4

→ 240 v = 3

→ v = 240/3

→ v = 80

$\bf\large{\underline{Hence:-}}$

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