SOLUTION: Jill walks from her home at 8km/h and gets a ride back home at 40km/h. If her total traveling time is half an hour, how long did it take Jill to walk to the movies and how far was

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Question 970136: Jill walks from her home at 8km/h and gets a ride back home at 40km/h. If her total traveling time is half an hour, how long did it take Jill to walk to the movies and how far was it?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in km she walks from home
Let +t+ = time in hours walking from home
+.5+-+t+ = time spent riding back
---------------------------------
Walking from home:
(1) +d+=+8t+
Riding back:
(2) +d+=+40%2A%28+.5+-+t+%29+
-----------------------
By substitution:
(2) +8t+=+20+-+40t+
(2) +48t+=+20+
(2) +t+=+5%2F12+ hrs
(2) +t+=+%28+5%2F12+%29%2A60+
(2) +t+=+25+ min
-----------------
(1) +d+=+8%2A%28+5%2F12+%29+
(1) +d+=+10%2F3+
(1) +d+=+3.333+
She walked 3.333 km in 25 min
-----------------------------
check:
(1) +d+=+8t+
(1) +3.333+=+8%2A%28+5%2F12+%29+
(1) +40+=+40+
and
(2) +d+=+40%2A%28+.5+-+t+%29+
(2) +3.333+=+40%2A%28+6%2F12+-+5%2F12+%29+
(2) +3.333+=+40%2F12+
(2) +40+=+40+
OK