Question

a man travels 600 kilometre partly by train and partly by car. if he covers 400 kilometre by train and the rest by car, it takes him 6 hours and 30 minutes .but if he travel 200 kilometre by train and rest by car he takes half an hour longer. find speed of train and that of car.​

Answer 1

Answer:

• speed of train = 100 km/h
• speed of Car = 80 km/h

Step-by-step explanation:

Let, speed of Train = x  and speed of Car = y

Total distance to be covered is 600 km

then,

Using formula ; Time = distance / speed

• According to the first condition when person covers 400 km by train and rest by Car it takes him 6 hrs 30 min means 13/2 hours.

→ 400/x  +  200/y  = 13/2

• According to second condition when person covers 200 km by train and rest by Car he takes half an hour longer.

→ 200/x + 400/y = (13/2) + (1/2)

→ 200/x + 400/y = 14/2

→ 200/x + 400/y = 7

Now,

we have two linear equations in two variables as,

400/x  +  200/y  = 13/2  ...eqn(1)

and

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

so,

Multiplying equation (1) by 2 both sides

→ 2(400/x) + 2(200/y) = 2(13/2)

→ 800/x   +  400/y  = 13  ...eqn(3)

subtracting equation (2) from equation (3) we will get,

→ 800/x  -  200/x  = 13 - 7

→ 600/x = 6

→ x = 600/6

→ x = 100 km/h

Putting value of x in eqn (2)

→ 200/x  +  400/y = 7

→ 200/(100)  +  400/y  = 7

→ 2 + 400/y  = 7

→  400/y  = 5

→ y = 80  km/h

Therefore,

• speed of train = 100 km/h
• speed of Car = 80 km/h.