SOLUTION: 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 a

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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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Fr + 2%2Fw = 1.3
and
6%2Fr + 4%2Fw = 1.6
:
multiply the 1st equation by 2, subtract the 2nd equation
16%2Fr + 4%2Fw = 2.6
6%2Fr + 4%2Fw = 1.6
------------------------------subtraction eliminates w, find r
10%2Fr + 0 = 1.0\
multiply both sides by r
r = 10 mph is the running speed
:
Find w
8%2F10 + 2%2Fw = 1.3
2%2Fw = 1.3 - .8
2%2Fw = .5
2 = .5w
w = 4 mph is the walking speed
:
:
Check in the 2nd equation
6%2F10 + 4%2F4 = 1.6