SOLUTION: a rod is chopped into 3 pieces. the first part is 3 times as long as the second piece,and the second piece is 3 times as long as the third piece. what fraction part of the rod is t

Algebra ->  Test -> SOLUTION: a rod is chopped into 3 pieces. the first part is 3 times as long as the second piece,and the second piece is 3 times as long as the third piece. what fraction part of the rod is t      Log On


   

Question 1149675: a rod is chopped into 3 pieces. the first part is 3 times as long as the second piece,and the second piece is 3 times as long as the third piece. what fraction part of the rod is the shortest piece?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
part1        3*3t=9t
part2        3t
part3         t
total       13t

Shortest part is part 3,  t.

Fraction of the original rod length, 1%2F13

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

If the third piece is x units long, then

   the second piece is 3x units long and
 
   the first piece is  3*(3x) units long.


If the total length of the rod is L, then


    x + 3x + 9x = L

    13x = L

      x = L%2F13.


ANSWER.  The shortest piece is 1%2F13 part of the rod length.


CHECK.  L%2F13 + %283%2AL%29%2F13 + %289%2AL%29%2F13 = %2813L%29%2F13 = L.