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.

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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) About Me  (Show Source):
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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%2Fr + 2%2Fw = .833
" If he runs 4km and walks 6km, his time is 1 hour 15mins."
4%2Fr + 6%2Fw = 1.25
:
Multiply the 1st equation by 3, subtract the 2nd equation
24%2Fr + 6%2Fw = 2.5
4%2Fr + 6%2Fw = 1.25
-----------------------------subtraction eliminates w, find r
20%2Fr = 1.25
1.25r = 20
r = 20%2F1.25
r = 16 km/hr, running speed
:
Find w using the 2nd equation, replace r with16
4%2F16 + 6%2Fw = 1.25
.25 + 6%2Fw = 1.25
6%2Fw = 1.25 -.25
6%2Fw = 1
w = 6 km/hr is his walking speed
:
:
Confirm this using the 1st original equation
8%2F16 + 2%2F6 =
.5 + .333 = .833 hr, which is 50 min