Question

1. A man travels 800 km partly by train and partly by car.If he covers 400 km by
train and rest by car, it takes him 14 hours. But, if he travels 200 km by train
and rest by car. he takes 3 hours longer. Find the speed of the car and that of
the train​

Answer 1

Answer:

The speed of the Train is 100 km/h and that of Car is 40 km/h.

Step-by-step explanation:

We are Given,

Total Distance = 800 km

Now,

Speed = Distance/Time

Time = Distance/Speed

Now,

Let the speed of train be 'x' km/h and speed of car be 'y' km/h

Case 1

Total distance = 800 km

Distance travelled by Train = 400 km

Then,

Distance travelled by Car = 800 - 400 = 400 km

We know that,

Time taken by Train + Time taken by Car = 14 hrs

Time = distance/speed

Thus,

(400/x) + (400/y) = 14

Let (1/x) = p and (1/y) = q

then,

400p + 400q = 14 ------- 1

Case 2

Total Distance = 800 km

Distance travelled by Train = 200 km

Distance travelled by Car = 800 - 200 = 600 km

So,

Time taken will be 3 hrs more than 14 hrs

= 14 + 3 = 17 hrs

Now,

Time taken by Train + Time taken by Car = 17

Time = distance/speed

thus,

200/x + 600/y = 17

But p = (1/x) and q = (1/y)

So,

200p + 600q = 17

Now, from eq.1 and eq.2,

400p + 400q = 14

200p + 600q = 17

Multiplying eq.1 with 1 and eq.2 with 2 to solve in elimination method,

400p + 400q = 14 ------ 3

400p + 1200q = 34 ------ 4

Subtracting eq.3 and eq.4 we get,

400p + 1200q = 34

- 400p + 400q = 14

- - -

————————————

0 + 800q = 20

————————————

800q = 20

q = 20/800

q = 1/40

Putting q = (1/40) in eq.1 we get,

400p + 400(1/40) = 14

400p + 10 = 14

400p = 14 - 10

p = 4/400

p = 1/100

But we say that,

p = (1/x)

(1/x) = 1/100

∴ x = 100 km/h

also,

q = 1/y

1/y = 1/40

∴ y = 40 km/h

Hence, the speed of the Train is 100 km/h and that of Car is 40 km/h.

Hope it helped and you understood it........All the best