Question 676562
A man travels 10km in 50mins if he runs for 8km and walks for 2km.
 If he runs 4km and walks 6km, his time is 1 hour 15mins.
 Find his running and walking speeds.
:
Let r = his running speed
Let w = his walking speed
:
Change 50 min to .833 hr; and 1 hr 15 min to 1.25 hrs

Write a time equation for each scenario; time = dist/speed
:
"A man travels 10km in 50mins if he runs for 8km and walks for 2km."
{{{8/r}}} + {{{2/w}}} = .833
" If he runs 4km and walks 6km, his time is 1 hour 15mins."
{{{4/r}}} + {{{6/w}}} = 1.25
:
Multiply the 1st equation by 3, subtract the 2nd equation
{{{24/r}}} + {{{6/w}}} = 2.5
{{{4/r}}} + {{{6/w}}} = 1.25
-----------------------------subtraction eliminates w, find r
{{{20/r}}} = 1.25
1.25r = 20
r = {{{20/1.25}}}
r = 16 km/hr, running speed
:
Find w using the 2nd equation, replace r with16
{{{4/16}}} + {{{6/w}}} = 1.25
.25 + {{{6/w}}} = 1.25
{{{6/w}}} = 1.25 -.25
{{{6/w}}} = 1
w = 6 km/hr is his walking speed
:
:
Confirm this using the 1st original equation
{{{8/16}}} + {{{2/6}}} = 
.5 + .333 = .833 hr, which is 50 min