Question 147121
Let {{{r[b]}}}= rate bicycling in mi/hr
Let {{{r[w]}}}= rate walking in mi/hr
It is given that {{{r[b] = r[w] + 10}}}
In words:
Total time for trip = (distance w/bicycle)/(rate on bicycle) +
(distance covered walking)/(rate walking)
{{{5 = 12/r[b] + 8/r[w]}}}
{{{5 = 12/(r[w] + 10) + 8/r[w]}}}
multiply both sides by {{{r[w]*(r[w] + 10)}}}
{{{5*r[w]*(r[w] + 10) = 12r[w] + 8*(r[w] + 10)}}}
{{{5*((r[w])^2 + 10r[w]) = 12r[w] + 8r[w] + 80}}}
{{{5*(r[w])^2 + 50r[w] = 20r[w] + 80}}}
{{{5*(r[w])^2 + 30r[w] - 80 = 0}}}
divide both sides by {{{5}}}
{{{r[w]^2 + 6r[w] - 16 = 0}}}
Just by looking at it,
{{{(r[w] + 8)(r[w] - 2) = 0}}}
{{{r[w] = -8}}}
{{{r[w] = 2}}} this is the one that makes sense (it's positive)
{{{r[b] = r[w] + 10}}}
{{{r[b] = 2 + 10}}}
{{{r[b] = 12}}}
He hikes 2 mi/hr and bikes 12 mi/hr
check:
{{{5 = 12/r[b] + 8/r[w]}}}
{{{5 = 12/12 + 8/2}}}
{{{5 = 1 + 4}}}
OK