Question

A man travels 600 km by train and partly by car. If he covers 400 km by train and the rest by car it takes him 6 hour 30 minutes. But if he travels 200 km by train and the rest by car he takes half an hr longer. Find the speed of the train and that of the car.

Answer 1

Hy mate.
I hope it will help you

Let x = peed of train

Let y = speed of car 

speed = distance / time
time = distance / speed

6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car

Train time + car time = total time

400 / x + 200 / y = 6.5 <== two equations and two unknowns
200 / x + 400 / y = 7 . . . . . . solve for x and y

400y + 200x = 6.5 xy
200y + 400x = 7 xy

400y - 6.5 xy = - 200x
200y - 7xy = - 400x

y ( 400 - 6.5x) = -200x
y ( 200 - 7x) = -400x

y (6.5x - 400) = 200x
y (7x - 200) = 400x

y = 200x / (6.5x - 400)
y = 400x / (7x - 200) * 

. . . since both equal y, the difference is zero

200x / (6.5x - 400) - 400x / (7x - 200) = 0

200x ( 7x - 200) - 400x (6.5x - 400) = 0

1400x^2 - 40000x - 2600x^2 + 160000x = 0

120000 x - 1200 x^2 = 0

100 - x = 0

x = 100 km / h = train speed

y = 400x / (7x - 200) . from *

y = 400 * 100 / (7 * 100 - 200) 

y = 80 km / h = car speed

So I think it will help you
Thank you ❤

Answer 2

Answer:

Speed of train is 100 km/hr and Speed of Car is 160 km/hr.

Step-by-step explanation:

Say,the speed of train be x km/hr

       the speed of car be y km/hr

According to the question,

400/x + 200/y = 6 + 30/60 ⇒ 400/x + 200/y = 13/2 ..................(1)

200/x + 400/y = 7 .........................(2)

put, 1/x = u and 1/y = v

we get,

400u + 200v = 13/2 ⇒ 800u + 400v = 13 ..................(3)

200u + 400v = 7 .......................(4)

Subtract (4) from (3),

800u - 200u = 13 - 7

600u = 6

u = 1/100

Substitute in (4),

800(1/100) + 400v = 13

8 + 400v = 13

400v = 13 - 8

400v = 5

v = 5/800

v = 1/160

Now, 1/x = 1/100 ⇒ x = 100

        1/y = 1/160 ⇒ y = 160

Therefore, Speed of train is 100 km/hr and Speed of Car is 160 km/hr.