SOLUTION: after running for a while at 8mph, Ludwig slowed to a walk at 4mph. If he traveled 68 miles in 12 hours, how far did he run and how far did he walk?

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Question 475299: after running for a while at 8mph, Ludwig slowed to a walk at 4mph. If he traveled 68 miles in 12 hours, how far did he run and how far did he walk?
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = miles that he ran
Let b = miles that he walked
given:
(1) +a+%2B+b+=+68+
(2) +a%2F8+%2B+b%2F4+=+12+
-----------------
Multiply both sides of (2) by 8
(2) +a+%2B+2b+=+96+
Subtract (1) from (2)
(2) +a+%2B+2b+=+96+
(1) +-a+-+b+=+-68+
+b+=+28+
and
(1) +a+%2B+b+=+68+
(1) +a+%2B+28+=+68+
(1) +a+=+68+-+28+
(1) +a+=+40+
Ludwig ran 40 miles and walked 28 miles
check answer:
(2) +a%2F8+%2B+b%2F4+=+12+
(2) +40%2F8+%2B+28%2F4+=+12+
(2) +5+%2B+7+=+12+
(2) +12+=+12+
OK

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
total distance = 68
running distance =x
running speed = 8 mph
walking distance = 68-x
walking speed = 4 mph
time running + time walking = 12
t=d/r
x/8 + (68-x)/4= 12
LCD = 8 multiply by 8
x+2(68-x)=8*12
x+136-2x=96
-x=96-136
-x=-40
x=40
distance run = 40 miles
Balance he walked
m.ananth@hotmail.ca