# Math Help - Distance problem

1. ## Distance problem

A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?

Equation: let x= walk rate
$\frac{32.4}{x}+\frac{32.4}{x+5.4}=12.6$

I think I set this equation up wrong...

2. ## Re: Distance problem

Originally Posted by theloser
A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?

Equation: let x= walk rate
$\frac{32.4}{x}+\frac{32.4}{x+5.4}=12.6$

I think I set this equation up wrong...
it's set up correctly.

3. ## Re: Distance problem

Originally Posted by skeeter
it's set up correctly.
It ends up to be $12.6x^2-64.8x-106.92$

I then multiply every by 100 $1260x^2-6480x-10692$

Then I factor everything by $36 ( 35x^2-180x-297 )$

Then I can't factor the binomials... Must have done something wrong... help please. Thanks Thanks

4. ## Re: Distance problem

Originally Posted by theloser
It ends up to be $12.6x^2-64.8x-106.92$

I then multiply every by 100 $1260x^2-6480x-10692$

Then I factor everything by $36 ( 35x^2-180x-297 )$

Then I can't factor the binomials... Must have done something wrong... help please. Thanks Thanks
what makes you think the quadratic should factor? sometimes they don't. nothing is wrong ... break out your calculator and use the quadratic formula.

5. ## Re: Distance problem

$32.4(x+5.4)+32.4x=12.6x(x+5.4)$
$(7x+27)(5x-18)=0$