SOLUTION: two people walk daily for exercise. One is able to maintain 4.0mph and the other only 3.5mph. The slow walker has a mile head start when the other begins, yet they finish together.

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Question 650348: two people walk daily for exercise. One is able to maintain 4.0mph and the other only 3.5mph. The slow walker has a mile head start when the other begins, yet they finish together. How far did each walk?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The slow walker has a head start of
1 mile
Let +d+ = the distance in miles
that the fast walker covers
--------------
Now time both of them after the head start
Let +t+ = the time for both
slow walker:
(1) +d+-+1+=+3.5t+
Fast walker:
(2) +d+=+4t+
-------------
Substitute (2) into (1)
(1) +4t+-+1+=+3.5t+
(1) +.5t+=+1+
(1) +t+=+2+
------------
and, since
(2) +d+=+4t+
(2) +d+=+4%2A2+
(2) +d+=+8+
Each walked the entire distance of 8 miles
check:
Slow walker's time during head start
was +t%5B1%5D+=+1%2F3.5+
+t%5B1%5D+=+2%2F7+
So his time for the whole 8 miles was +2%2F7+%2B+2+=+16%2F7+ hrs
+d+=+3.5%2A%2816%2F7%29+
+d+=+%287%2F2%29%2A%2816%2F7%29+
+d+=+8+
OK