Question

A man travels 300 km partly by train and partly by car. He takes 4 hours if the
travels 60 km by train and the rest by car If he travels 100 km by train and the
remaining by car he takeS 10 minutes longer. Find the speeds of the train and the
car separately​

Answer 1

Answer:

Speed of train = 60 km/hr

Speed of car = 80 km/hr

Step-by-step explanation:

Given:

• A man travels 300 km partly by train and partly by car
• He takes 4 hours if he travels 60 km by train and rest by car.
• If he travels 100 km by train and rest by car he takes 10 minutes longer

To Find:

• Speed of train
• Speed of car

Solution:

Let the speed of the train be a km/hr and speed of the car be b km/hr.

By first case given,

Distance travelled by train = 60 km

Distance travelled by car = (300 - 60) = 240 km

Time taken = 4 hours

We know that,

Time = Distance/Speed

Hence,

$\sf \dfrac{60}{a} +\dfrac{240}{b} =4---(1)$

By the second case given,

Distance travelled by train = 100 km

Distance travelled by car = (300 - 100) = 200 km

Time taken  = 4 hours + 10 mins = (4 + 10/60) hours = 25/6 hours

Therefore,

$\sf \dfrac{100}{a} +\dfrac{200}{b} =\dfrac{25}{6} ---(2)$

Now let 1/a = x and 1/b = y

Hence equation 1 and 2 changes to

60 x + 240 y = 4 -----(3)

100 x + 200 y = 25/6---(4)

Multiply equation 3 by 5 and equation 4 by 3

Hence,

300 x + 1200 y = 20

300 x + 600 y = 25/2

Solving the above equations by elimination method,

600 y = 15/2

y = 15/1200

y = 1/80

Substitute the value of y in equation 3,

60 x + 3  = 4

60 x = 1

x = 1/60

Now we know that,

1/a = x, 1/x = a and 1/b =y, 1/y = b

Hence,

a = 60 km/hr = Speed of the train

b = 80 km/hr = Speed of the car

Hence the speed of the train is 60 km/hr and speed of the car is 80 km/hr.

Answer 2

Answer:

Speed of train= 15km/h

Speed of car = 1200/41km/h

Step-by-step explanation:

Given,

Total distance=300km

Distance covered by train=100km

AND

Car take 10 minutes more time than train in

cover distance.

Train cover 60km in 4 hours.

So,Distance covered by car = 200km

Speed of train = 15km/h (60/4)

Since, Speed of train= 15km/h

So, time taken in cover 100km= 100/15

= 20/3 hrs

So, time taken by car = 20/3+1/6 (10min=1/6hr)

= (40+1)/6

= 41/6 hrs

So, Speed of car = 200/(41/6) (s= d/t)

= 200×6/41

= 1200/41 km/h