SOLUTION: amin has completed one third of his cycling race. he has 18km to go to reach the halfway mark. howmany kilometres he still has to cycle to the finish

Question 1027057: amin has completed one third of his cycling race. he has 18km to go to reach the halfway mark. howmany kilometres he still has to cycle to the finish
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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