Question 1054995
you've got 3 equations that need to be solved simultaneously.


they are:


R * T = D


(R + 1/2) * (4/5 * T) = D


(R - 1/2) * (T + 2.5) = D


since all expressions on the left side of each equation are all equal to D, they can all be set equal to each other.


since R * T is easier to deal with, we'll use that as one of the equal pairs.


start with:


R * T = (R + 1/2) * (4/5 * T)


simplify to get:


R * T = 4/5 * R * T + 1/2 * 4/5 * T


divide both sides of this equation by T to get:


R = 4/5 * R + 1/2 * 4/5


subtract 4/5 * R from both sides of this equation to get:


R - 4/5 * R = 4/10


combine like terms to get:


1/5 * R = 4/10


multiply both sides of this equation by 5 to get:


R = 20/10 = 2


now use R * T = D and (R - 1/2) * (T + 2.5) = D


set them equal to each other to get:


R * T = (R - 1/2) * (T + 2.5)


replace R with 2 to get:


2 * T = 3/2 * (T + 2.5)


simplify to get:


2 * T = 3/2 * T + 3/2 * 2.5


subtract 3/2 * T from both sides of this equation to get:


1/2 * T = 3/2 * 2.5


multiply both sides of this equation by 2 to get:


T = 3 * 2.5 which results in T = 7.5


you have R = 2 and T = 7.5


R * T = D becomes 2 * 7.5 = D which results in D = 15.


(R + 1/2) * (4/5 * T) = D becomes 2.5 * 4/5 * 7.5 = D which becomes 2.5 * 30 / 5 = D which becomes 2.5 * 6 = D which results in D = 15.


(R - 1/2) * (T + 2.5) = D becomes 3/2 * 10 = D which results in D = 15.


all 3 equations are satisfied when R = 2 and T = 7.5.


your solution is that the distance is 15 kilometers.