le agrees to build a fence for $1200. Takes him 3 days longer than expected and he earns $22.50 less per day than expected. In how many days did he expect to complete the fence?

Question

this is a question from rational expressions practice worksheet in my grade 11 math class .

Answer 1

He expected to complete the fence in x days at $y per day, so xy=1200.

But he completed the fence (at the same cost) in x+3 days at a cost of y-22.50 dollars a day, so (x+3)(y-22.5)=1200,

xy-22.5x+3y-67.5=1200.

But xy=1200, so:

-22.5x+3y-67.5=0.

y=1200/x, therefore:

-22.5x+3600/x-67.5=0.

Multiplying through by -x/22.5:

x²-160+3x=0, or x²+3x=160.

Completing the square:

x²+3x+9/4=160+9/4=649/4.

(x+3/2)²=649/4.

So, x=√649/2-3/2=12.74-1.5=11.24 days approx.

He expected to take about 11.24 days to complete the job at $106.78 per day.