Question 914369
A man running for 8 miles and walking for 2 miles covers 10 miles in 1 hr.18 mins.
 If he runs 6 miles and walk 4 miles, the distance takes him 1 hr. 36 mins.
 What are his running and walking speed?
:
let  w = speed walking
let  r = speed running
:
Change 1 hr 18 min to hrs. 1 + 18/60 = 1.3 hrs
Change 1 hr 36 min to hrs. 1 + 36/60 = 1.6 hrs
:
A time equation for each scenario; time = dist/speed
{{{8/r}}} + {{{2/w}}} = 1.3
and
{{{6/r}}} + {{{4/w}}} = 1.6
:
multiply the 1st equation by 2, subtract the 2nd equation
{{{16/r}}} + {{{4/w}}} = 2.6
{{{6/r}}}  + {{{4/w}}} = 1.6
------------------------------subtraction eliminates w, find r
{{{10/r}}} + 0 = 1.0\
multiply both sides by r
r = 10 mph is the running speed
:
Find w
{{{8/10}}} + {{{2/w}}} = 1.3
{{{2/w}}} = 1.3 - .8
{{{2/w}}} = .5
2 = .5w
w = 4 mph is the walking speed
:
:
Check in the 2nd equation
{{{6/10}}}  + {{{4/4}}} = 1.6