SOLUTION: A piece of iron rod costs P60. If the rod was 2 meter shorter and each meter costs P1 more, the cost would remain unchanged. What is the length of the rod?

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Question 1186516: A piece of iron rod costs P60. If the rod was 2 meter shorter and each meter costs P1 more, the cost would remain unchanged. What is the length of the rod?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!

             PRICE           LENGTH           COST

               60/x            x              60

               60/(x-2)        x-2            60

Difference         1

highlight_green%2860%2F%28x-2%29-60%2Fx=1%29
Simplify and solve for x.
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.
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Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
A piece of iron rod costs P60. If the rod was 2 meter shorter and each meter costs P1 more,
the cost would remain unchanged. What is the length of the rod?
~~~~~~~~~~~~~~~ 


Let x be the length of the rod, in meters.

Then the hypothetical length of the rod is (x-2) meters.


Next, we write this equation


    60%2F%28x-2%29 - 60%2Fx = 1,     (1)


saying that the cost of 1 meter of hypothetical road is P1 more than the cost of 1 meter of the real rod.


Now I will show you the way to solve this equation, which you newer saw before.


The difference  60%2F%28x-2%29 - 60%2Fx  is equal to  %282%2A60%29%2F%28%28x-2%29%2Ax%29,


So, equation (1) takes the form


    %282%2A60%29%2F%28%28x-2%29%2Ax%29 = 1,


which implies


    120 = x*(x-2).


Thus the number 120 is the product of two numbers, that differ in 2 units.


You momentarily/instantly GUESS these numbers MENTALLY:  they are 12 and 10.


ANSWER.  The length of the road is 12 meters.

Solved.