A man drives from his house to the station. If he drives at the rate of 10 Km/hour, he reaches the station at 6 p.m. If he drives at 15 Km/hour, he would reach the station at 4 p.m. At what speed, in kilometers per hour, should drive so as to reach the station at 5 p.m.?
distance = d
say he leaves at n oclock in the afternoon
d = 10 km/hr * (6-n) hr
d = 15 km/hr * (4-n) hr
so what is n, his departure time ?
subtract
0 = 10(6-n) - 15 (4-n)
60 - 15 n = 60 - 10 n
n = 0, noon
d = 60 km
60 = v (5 - 0)
v = 12 km/hr
Well, it seems like this man is quite the speed racer! If he drives at 10 km/h, he reaches the station at 6 p.m., and if he drives at 15 km/h, he reaches the station at 4 p.m. So, to reach the station at 5 p.m., he needs to find the perfect speed.
Let me think... If he drives at 10 km/h, he needs an extra hour to reach the station at 5 p.m. And if he drives at 15 km/h, he reaches the station an hour earlier at 4 p.m.
To find the speed he needs to drive at to reach the station at 5 p.m., we can assume that the distance from his house to the station is the same in both scenarios. That means, in one hour, he covers 5 km more when driving at 15 km/h compared to 10 km/h.
So, to cover this extra distance of 5 km in one hour, he should drive at a speed of 5 km/h.
Therefore, to reach the station at 5 p.m., he should drive at a speed of 10 + 5 = 15 km/h.
Hope that helps, and remember to always buckle up before driving at clown-like speeds!
To find the required speed, we can first calculate the time it takes for the man to drive from his house to the station at both 10 km/h and 15 km/h.
Let's denote the distance from the man's house to the station as 'd'.
Step 1: Calculate the time taken at 10 km/h:
Time = Distance / Speed
Time = d / 10
Step 2: Calculate the time taken at 15 km/h:
Time = Distance / Speed
Time = d / 15
According to the given information, when the man drives at 10 km/h, he reaches the station at 6 p.m. and when he drives at 15 km/h, he reaches the station at 4 p.m.
Step 3: Convert the given time into minutes:
6 p.m. = 6 * 60 = 360 minutes
4 p.m. = 4 * 60 = 240 minutes
Step 4: Set up the equations:
d / 10 = 360
d / 15 = 240
Step 5: Solve for 'd':
d = 10 * 360
d = 3600
d = 15 * 240
d = 3600
Since both equations equal the same value of 'd', it means the distance between the man's house and the station is 3600 km.
Step 6: Calculate the required speed to reach the station at 5 p.m.:
Time = Distance / Speed
Time = 3600 / Speed
Since he wants to reach the station at 5 p.m., we need to find the speed at which he can cover 3600 km in 8 hours (from 4 p.m. to 5 p.m.):
Step 7: Set up the equation:
8 = 3600 / Speed
Step 8: Solve for Speed:
Speed = 3600 / 8
Speed = 450 km/hour
Therefore, the man should drive at a speed of 450 kilometers per hour to reach the station at 5 p.m.
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.