Question 299963
If bill rides his bike 3 miles to Fred's house and then walks with Fred the
 remaining 1 mile to school, it will take him 30 minutes. 
But if he rides the entire distance, it will take him only 20 minutes.
 what is his walking and biking speed?
:
let b = biking speed
let w = walking speed
:
Write two time equations; time = dist/speed:
ride and walk equation
{{{3/b}}} + {{{1/w}}} = {{{1/2}}}
and
ride only equation
{{{4/b}}} = {{{1/3}}}
Cross multiply
b = 4*3
b = 12 mph is the biking speed
:
Find the walking speed using the 1st equation
{{{3/12}}} + {{{1/w}}} = {{{1/2}}}
multiply by 12w, results:
3w + 12 = 6w
12 = 6w - 3w
3w = 12
w = 4 mph is the walking speed
:
;
Check solution using the 1st equation
{{{3/12}}} + {{{1/4}}} = 
{{{1/4}}} + {{{1/4}}} = {{{1/2}}}