# Distance problem

• Jul 10th 2011, 05:00 PM
theloser
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...
• Jul 10th 2011, 05:06 PM
skeeter
Re: Distance problem
Quote:

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.
• Jul 10th 2011, 05:14 PM
theloser
Re: Distance problem
Quote:

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
• Jul 10th 2011, 05:41 PM
skeeter
Re: Distance problem
Quote:

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.
• Jul 10th 2011, 05:44 PM
Re: Distance problem

$32.4(x+5.4)+32.4x=12.6x(x+5.4)$

This gives eventually

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