Edna and Nancy leave the house of a common friend at the same time and walk for 4 hours. Edna walks due east at the average rate of 4 kilometers per hour and Nancy walks due north at the average rate of 3 kilometers per hour. What is the straight-line distance between them in kilometers, at the end of the 4 hours?
on walked 12km, and one walked 16km at right angles.
Isn't this a 3-4-5 right triangle?
Yes, it probably is, but I have a hard time solving problems that involve 3-4-5 triangles or anything similar to that.
Wow, Edna and Nancy walk for 16 km and 12 km??
Can't be in 2008, they would get in their SUV's for sure, lol
I see a right-angled triangle with sides 12 and 16, where you have to find the hypotenuse.
Think Pythagoras !
lol, thank you. I understand the problem now.
12
To find the straight-line distance between Edna and Nancy, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider Edna's and Nancy's paths as forming the legs of a right triangle, with the distance between them being the hypotenuse. Let's call this distance d.
First, let's determine the distances each person has traveled. Edna has walked for 4 hours at a rate of 4 kilometers per hour, so she has traveled 4 x 4 = 16 kilometers.
Nancy has also walked for 4 hours but at a rate of 3 kilometers per hour, so she has traveled 4 x 3 = 12 kilometers.
Now, we can use these distances as the lengths of the legs of the right triangle.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
d^2 = (16^2) + (12^2)
Simplifying:
d^2 = 256 + 144
d^2 = 400
Taking the square root of both sides:
d = √400
d = 20 kilometers
Therefore, the straight-line distance between Edna and Nancy, at the end of the 4 hours, is 20 kilometers.