To find the speed at which the man should drive in order to reach the station at 5 p.m., we can use the concept of relative speed.
Let's start by finding the distance between the man's house and the station. We know that he reaches the station at 6 p.m. when driving at a speed of 10 km/hour, and at 4 p.m. when driving at a speed of 15 km/hour. Therefore, the time it takes him to travel from his house to the station is 2 hours when driving at 10 km/hour (6 p.m. - 4 p.m.) and 4 hours when driving at 15 km/hour (6 p.m. - 2 p.m.).
Now, let's calculate the distance using the formula: Distance = Speed × Time.
When driving at 10 km/hour for 2 hours, the distance covered is 10 km/hour × 2 hours = 20 km.
When driving at 15 km/hour for 4 hours, the distance covered is 15 km/hour × 4 hours = 60 km.
To find the speed at which the man should drive to reach the station at 5 p.m., we first need to determine the time it takes to cover the distance of 60 km. Since he currently takes 4 hours to cover this distance, we can assume that the time will be less than 4 hours, as he needs to reach the station one hour earlier at 5 p.m.
Let's assume the speed at which the man should drive to reach the station at 5 p.m. is x km/hour. We can now calculate the time using the formula: Time = Distance / Speed.
Therefore, the time taken to cover 60 km at the speed of x km/hour is 60 km / x km/hour = 5 p.m. - 2 p.m. = 3 hours.
Now, we have two equations:
Equation 1: 20 km / 10 km/hour = 2 hours
Equation 2: 60 km / x km/hour = 3 hours
We need to find the value of x. Cross-multiplying Equation 2, we get:
60 km = 3 hours × x km/hour
60 km = 3x km
x km/hour = 60 km / 3
x km/hour = 20 km/hour
Therefore, the man should drive at a speed of 20 km/hour in order to reach the station at 5 p.m.