A son and his father take a daily walk up a hill. It is 1.5 km to the top of the hill. As the father gets older he can only walk half the speed of his son. So they start together but the father trails his son. The father reaches the halfway point when the son is at the top. The father continues to walk up as the son begins to walk down. When they meet the father turns around and walks back down the hill with his son. How far does the father walk?
To find out how far the father walks, we need to analyze the situation step by step. Let's break it down:
1. The father and son start at the bottom of the hill together.
2. The father walks at half the speed of his son, so he will take twice as long to cover the same distance.
3. The son reaches the top of the hill while the father is still at the halfway point.
4. At this point, the son starts walking back down the hill towards the father.
5. When they meet on the hill, the father turns around and walks back down with his son.
6. Since the father walked halfway up the hill before turning around, he will need to walk the same distance back down.
To calculate the distance the father walks, let's consider the time it takes for the father and son to cover their respective distances.
Let's assume the son's speed is S km/hr, so the father's speed is (S/2) km/hr.
The time taken by the son to reach the top of the hill (1.5 km) is given by:
Time_taken_son = Distance / Speed = (1.5 km) / S km/hr
At the same time, the father travels half the distance (0.75 km) and then turns around. The time taken by the father is given by:
Time_taken_father = Distance / Speed = (0.75 km) / (S/2) km/hr
Since the son and father meet at the halfway point, the total time taken by the son to reach the halfway point and return is the same as the time taken by the father to reach the top of the hill.
So, we have the equation:
Time_taken_son = Time_taken_father
Substituting the values, we get:
(1.5 km) / S km/hr = (0.75 km) / (S/2) km/hr
Now, let's solve for S by cross-multiplying:
(1.5 km) * (S/2) = (0.75 km) * S
0.75S = 1.5
S = 1.5 / 0.75
S = 2 km/hr
Now that we have the son's walking speed, we can calculate the time taken by the son to reach the top of the hill:
Time_taken_son = Distance / Speed = (1.5 km) / (2 km/hr) = 0.75 hours
Since the father walks at half the speed, the time taken by the father to reach the top of the hill is twice as long:
Time_taken_father = 2 * 0.75 hours = 1.5 hours
Therefore, the father walks for 1.5 hours, covering a distance of:
Distance = Speed * Time = (S/2) km/hr * 1.5 hours = (2 km/hr) * 1.5 hours = 3 km
Hence, the father walks a distance of 3 km.