SOLUTION: 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 1h 15mins. find his running and walking speed.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 1h 15mins. find his running and walking speed.       Log On


   

Question 723994: 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 1h 15mins. find his running and walking speed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 1h 15mins.
find his running and walking speed.
:
Change 50 min to 5/6 hr
Change 1 hr 15 min to 5/4 hr
:
Let r = his running speed in km/hr
Let w = his walking speed
:
Write a time equation for each scenario; time = dist/speed
:
8%2Fr + 2%2Fw = 5%2F6
and
4%2Fr + 6%2Fw = 5%2F4
:
Multiply the above by 2 and subtract the 1st equation
8%2Fr + 12%2Fw = 10%2F4
8%2Fr + 2%2Fw = 5%2F6
--------------------------------- subtraction eliminates r, find w
0 + 10%2Fw = 10%2F4 - 5%2F6
multiply by 12w, resulting in
12(10) = 3w(10) - 2w(5)
120 = 30w - 10w
120 = 20w
w = 120/20
w = 6 km/hr walking
:
Replace w with 6 in the 1st equation
8%2Fr + 2%2F6 = 5%2F6
8%2Fr = 5%2F6 - 2%2F6
8%2Fr = 3%2F6
cross multiply
3r = 8 * 6
3r = 489
r = 48/3
r = 16 km/hr running
:
;
Check solution in the 2nd equation
4%2F16 + 6%2F6 = 5%2F4