# A takes 3 hours more than B to walk 30 km. But if A doubles his pace, he is ahead of B by 3 /2 hours. Find their speed of walking.

The question is based on applications of linear equations.

## Answer: The speed of walking of A is 10/3 km/h and that of B is 5 km/h.

Let us frame the equations according to the data and thereby find their speed of walking

**Explanation:**

The total distance is 30 Km.

Let the speed of A be x km/h and the speed of B be y km/h.

⇒ The time taken by A will be 30/x hours

⇒ The time taken by B will be 30/y hours

Given that, A takes 3 hours more than B to walk 30 km

Then, 30/x = (30/y) + 3

30/x - 30/y = 3

(30/x) - 3 = 30/y

30/y = (30/x) - 3 -------------------> equation (1)

Also given, if A doubles his pace, he is ahead of B by 3 /2 hours

Then, 30/y - 30/2x = 3/2

30/y - 15/x = 3/2 -------------------> equation (2)

Now let's solve these linear equations to get the values of x and y by substitution method:

30/y - 15/x = 3/2

[ (30/x) - 3 ] - 15/x = 3/2

(30/x) - 3 - 15/x = 3/2

(30 - 15) / x = 3/2 + 3

15/x = (3 + 6)/2

15/x = 9/2

9x = 15 × 2

9x = 30

**x = 10/3**

From equation(1):

30/y = (30/x) - 3

30/y = [ 30/(10/3) ] - 3

30/y = 9 - 3

30/y = 6

y = 30/6

**y = 5**