A takes 3 hours more than B to walk 30 km. But if A doubles his pace, he is ahead of B by one and half hrs. Find their speed of walking.

Sure, let's solve this step by step.

Step 1: Let's denote the speed of B as 'b' km/hr and the speed of A as 'a' km/hr.

Step 2: From the problem, we know that the time taken by A to walk 30 km is 3 hours more than B. We can express this as: 30/a = 30/b + 3

Step 3: We also know that if A doubles his pace, he is ahead of B by one and a half hours. This can be expressed as: 30/(2a) = 30/b - 1.5

Step 4: Now we have a system of two equations, and we can solve it to find the values of 'a' and 'b'.

Step 5: Multiply the first equation by 2 and subtract the second equation from the result: 2*(30/a) - 30/(2a) = 2*(30/b + 3) - (30/b - 1.5) 60/a - 15/a = 60/b + 6 - 30/b + 1.5 45/a = 30/b + 7.5 45/a = 30/b + 15/2 Multiply by 2ab: 90b = 60a + 15ab 90b = 75a + 15ab 15b = 15a + 3ab b = a + 0.2a*b

Step 6: Substitute b from the first equation into this equation: a + 0.2a*(30/a + 3) = a 0.2a*(33/a) = 0 a = 0

This is a contradiction, which means that the problem does not have a solution. The speeds of A and B cannot be determined from the given conditions.