Question 1027057
he has completed 1/3 of the race.
he has 18 km more to go to reach the halfway mark.


let x = the length of the race.


you get 1/3 * x + 18 = 1/2 * x


this equation says that 1/3 * the length of the race + 18 is equal to half the length of the race.


solve as follows:


start with 1/3 * x + 18 = 1/2 * x


subtract 1/3 * x from both sides of the equation to get 18 = 1/2 * x - 1/3 * x


1/2 is the same as 3/6 and 1/3 is the same as 2/6.


the equation becomes 18 = 3/6 * x - 2/6 * x.


combine like terms to get 18 = 1/6 * x


multiply both sides of the equation by 6 to get 18 * 6 = x


simplify to get x = 108.


you are given that 1/3 * the length of the race + 18 is equal to 1/2 * the length of the race.


since the length of the race is 108, then 1/2 of 108 is equal to 54.


1/3 * the length of the race is equal to 108/3 = 36.


add 18 to that and you get 54 which is equal to 1/2 of the length of the race.


since he finished 1/3 of the race, then he has 2/3 of the length of the race to go.


2/3 * 108 = 2 * 36 = 72 kilometers left to go.


that's your solution.


72 + 36 = 108, so the solution looks good.