can you help me?
fred leaves his house at 2pm and travels due north at 30km/hour. ron has been traveling due west at 20km/hour and arrives at fred's house at 3pm. where were they closest together?
Of course, I can help you with that. To find out where Fred and Ron were closest together, we need to determine their positions at different times and calculate their distance.
Let's start by determining Fred's position at 3pm. Since Fred travels due north at a constant speed of 30 km/h, we can calculate his distance traveled in one hour:
30 km/h * 1 hour = 30 km
Therefore, at 3pm, Fred is 30 km north of his starting point.
Now, let's determine Ron's position at 3pm. Ron has been traveling due west at a constant speed of 20 km/h for a total of 1 hour. So, Ron has traveled:
20 km/h * 1 hour = 20 km
Therefore, at 3pm, Ron is 20 km to the west of Fred's house.
To find out where they were closest together, we can imagine a right-angled triangle formed by the positions of Fred's house, Fred at 3pm, and Ron at 3pm. We want to find the point on the triangle that is closest to Fred's house.
Since Fred's house is directly north of Fred at 3pm, we only need to find the horizontal distance between Ron at 3pm and Fred's house. This distance is the remaining side of the right-angled triangle, which can be calculated using the Pythagorean theorem.
The distance between Ron at 3pm and Fred's house is:
distance = square root of ((30 km)^2 + (20 km)^2)
Calculating this distance, we get:
distance = square root of (900 km^2 + 400 km^2) = square root of 1300 km^2
To simplify the calculation, we can approximate the square root of 1300 as approximately 36.06 km.
Therefore, Fred and Ron were closest together approximately 36.06 km from Fred's house.
I hope this explanation helps. Let me know if you have any further questions!