Let’s denote the speed of A as vA km/h and the speed of B as vB km/h.
From the problem, we know that A takes 3 hours more than B to walk 30 km. Therefore, we can set up the following equations based on the formula: time = distance/speed.
For A:
- Time taken by A = 30/vA hours
For B:
- Time taken by B = 30/vB hours
According to the given information:
Time taken by A = Time taken by B + 3 hours
This leads to the equation:
30/vA = 30/vB + 3Rearranging gives us:
30/vA - 30/vB = 3Next, we learn that if A doubles his speed, he finishes 2 hours before B:
- Time taken by A at double speed = 30/(2vA) hours
- Time taken by B remains the same = 30/vB hours
The relationship then states:
Time taken by A (at double speed) = Time taken by B – 2 hours
30/(2vA) = 30/vB - 2Now, we have two equations:
Depending on what you require, we can solve these equations to find the desired speeds. Let’s solve them step-by-step.
1) From the first equation, we can express one speed in terms of the other:
30/vA - 30/vB = 3
=> 10(vB - vA) = vA vB 2) From second equation:
30/(2vA) + 2 = 30/vB Simplifying yields
15/vA + 2 = 30/vBWe can express vB in terms of vA:
1/vB= (1/15+2)/vABased on these equations, we can substitute values and solve simultaneously. Upon doing so, we find:
- vA = 3 km/h
- vB = 5 km/h
Thus, the required speeds of walking are A’s speed is 3 km/h and B’s speed is 5 km/h.