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 1 hour 15mins. Find his running and walking speeds.

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.
Answer by ankor@dixie-net.com(22740) (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 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."
+ = .833
" If he runs 4km and walks 6km, his time is 1 hour 15mins."
+ = 1.25
:
Multiply the 1st equation by 3, subtract the 2nd equation
+ = 2.5
+ = 1.25
-----------------------------subtraction eliminates w, find r
= 1.25
1.25r = 20
r =
r = 16 km/hr, running speed
:
Find w using the 2nd equation, replace r with16
+ = 1.25
.25 + = 1.25
= 1.25 -.25
= 1
w = 6 km/hr is his walking speed
:
:
Confirm this using the 1st original equation
+ =
.5 + .333 = .833 hr, which is 50 min

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