Question 342339
The formula we will use is R * T = D where R = rate of speed in km/hr, T = time in hr, and D = distance in km.


We let T = total time it took to get there and back.
We let D = total distance from there and back.


Going to her friend's house, we let x = the amount of time it took, and we let D/2 = the distance she traveled, and we let 16 = the rate of her speed.


The formula for her going is 16 * x = D/2.


Coming back from her friend's house, we let T-x = the amount of time it took, and we let D/2 = the distance she traveled, and we let 80 = the rate of her speed in her friend's car.


The formula for her coming back is 80 * (T-x) = D/2.


Both of these formulas are equal to D/2, so they are both equal to each other.


We get:


16 * x = 80 * (T - x)


We expand these formulas by removing parentheses to get:


16 * x = 80 * T - 80*x


We add 80*x to both sides of this equation to get:


16*x + 80*x = 80*T


We combine like terms to get:


96*x = 80*T


We know that T = 3 hours because that's what we were given.


Our formula becomes:


96*x = 80 * 3


This becomes 96 * x = 240


We divide both sides of this equation by 96 to get:


x = 240/96 which makes x = 2.5 hrs.


Since T is equal to x + (T-x), then (T-x) has to be .5 hrs.


Now that we know x and T-x, we can solve for D/2.


In the formula where Ava goes to her friend's house, we get:


16 * x = D/2 becoming 16 * 2.5 = D/2 which makes D/2 equal to 40 km.


In the formula where Ava comes back from her friend's house, we get:


80 * (T-x) = D/2 becoming 80 * .5 = D/2 which makes D/2 equal to 40 km.


Both formulas point to the same distance as they should.


The distance from Ava'a house to her friend's house is equal to 40 km.


40 km = D/2


D is the distance there and back.


D is therefore equal to 80 km.


But you didn't want D.


You wanted D/2 which is the distance from Ava's hour to her friend's house.


Your answer is therefore equal to 40 km.