Question

A man travels 600km partly train and by car lf he covers 400km by train and rest by car it takes him 6hours 30min but if he travels 200km by a train and rest by car he takes half an hour longer find the speed of
train and that of car ​

Answer 1

PLS MARK ME AS BRAINLIEST AND FOLLOW ME BACK

Answer 2

Answer:

➞ Speed of the train = 100 km/hr

➞ Speed of the car = 80 km/hr

Step-by-step explanation:

Given:

• Total distance travelled by the man = 600 km

• If the man travels 400 km by train and rest by car it takes him 6 hours and 30 minutes.
• If the man travels 200 km by train and the rest by car, he takes half an hour longer.

To Find:

• Speed of the train
• Speed of the car

Solution:

Let us assume the speed of the train as x km/hr.

Let the speed of the train be y km/hr.

By first case given,

Time taken to travel by train + Time taken to travel by car = 6 hours 30 minutes.

But we know that,

Time = Distance/Speed

Therefore,

$\tt \dfrac{400}{x} +\dfrac{200}{y} =6.5 \:hours----(1)$

Now by second case given,

Time taken to travel by train + Time taken to travel by car = 6.5 + 30 minutes.

Hence,

$\tt \dfrac{200}{x} + \dfrac{400}{y} =7\:hours----(2)$

Now let 1/x = p and 1/y = q

Hence equation 1 and 2 changes to,

400p + 200q = 6.5-------(3)

200p + 400q = 7----------(4)

Multiply equation 3 by 2

800p + 400q = 13-------(5)

Solving equation 4 and 5 by elimination method,

-600p = -6

p = 1/100

Substitute the value of p in equation 4,

200 × 1/100 + 400q = 7

2 + 400q = 7

400q = 5

q = 5/400

q = 1/80

But we know that 1/x = p, x = 100 km/hr

Therefore the speed of the train is 100 km/hr.

Also, 1/y = q, y = 80 km/hr

Hence speed of the car is 80 km/hr.