In covering a distance of 30km.'A' takes 2 hours more than 'B'. If 'A' doubles his speed,he would take 1 hour less than 'B' . find their rates of walking.
To solve this problem, let's assume 'A' walks at a rate of x km/h and 'B' walks at a rate of y km/h. We can use the formula Speed = Distance / Time to find their rates of walking.
According to the given information, 'A' takes 2 hours more than 'B' to cover 30 km. So, we can write the following equation:
30 / x = 30 / y + 2
Now, if 'A' doubles their speed (2x), they would take 1 hour less than 'B' to cover the same distance. We can represent this in equation form as:
30 / (2x) = 30 / y - 1
Now, we have two equations:
1) 30 / x = 30 / y + 2
2) 30 / (2x) = 30 / y - 1
To find the rates of walking for 'A' and 'B', we need to solve these two simultaneous equations.
First, let's simplify equation 1 by multiplying both sides by xy:
30y = 30x + 2xy
Now, let's simplify equation 2 by multiplying both sides by 2xy:
60x = 30y - 2xy
Next, let's rearrange equation 1:
30y - 2xy = 30x
We can rewrite this equation as:
30y - 30x = 2xy
Now, let's add this equation to equation 2:
(30y - 2xy) + 60x = 30y - 30x
Simplifying this equation, we get:
60x - 30x = 30y - 30y + 2xy
30x = 2xy
Now, we can divide both sides of the equation by 2x:
30 / 2 = y
15 = y
Substituting this value back into equation 1, we can solve for x:
30 / x = 30 / 15 + 2
Simplifying, we get:
2 = 2 / x
Multiplying both sides by x, we get:
2x = 2
Dividing both sides by 2, we get:
x = 1
Therefore, 'A' walks at a rate of 1 km/h and 'B' walks at a rate of 15 km/h.