Problem Statement:

A takes two hours more than be to cover 20 km. If a doubles his speed he would take 1 hr less than b. Find the speed of both.

Solution:

Let's assume that the speed of B is x km/hr. Then the speed of A would be (x-2) km/hr as he takes two hours more than B to cover the same distance.

Now, let's calculate the time taken by A and B to cover 20 km:

Time taken by A: 20/(x-2) hours

Time taken by B: 20/x hours

According to the problem, if A doubles his speed, he would take 1 hour less than B to cover the same distance. Therefore, the time taken by A would be equal to the time taken by B minus 1 hour. So, we can write:

20/x = 20/(2(x-2)) + 1

Simplifying the above equation, we get:

20/x = 10/(x-2) + 1

Multiplying both sides by x(x-2), we get:

20(x-2) = 10x + x(x-2)

Simplifying the above equation, we get:

x^2 - 8x - 40 = 0

Solving the above quadratic equation, we get:

x = 10 or x = -4

Since the speed cannot be negative, we can ignore the negative value of x. Therefore, the speed of B is 10 km/hr.

Using the speed of B, we can calculate the speed of A as:

Speed of A = 10 - 2 = 8 km/hr

Therefore, the speed of A is 8 km/hr and the speed of B is 10 km/hr.

Speed of A - 5 km/hSpeed of B - 10 km/h