SOLUTION: Jana ran the first 3 1/2 of a 5-mile race in 1/3. What is her average rate in miles per hour for the first part of the race and how do I solve the problem??

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Question 961399: Jana ran the first 3 1/2 of a 5-mile race in 1/3. What is her average rate in miles per hour for the first part of the race and how do I solve the problem??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
[ distance ] = [ rate ] x [ time ]
+d+=+r%2At+
Divide both sides by +t+
+r+=+d+%2F+t+
---------------
given:
+d+=+3+%2B+1%2F2+
+t+=+1%2F3+
-----------------
Note that:
+%28+2d+%29+%2F+%28+2t+%29+=+d%2Ft+,
so, I can say:
+r+=+7+%2F+%28+2%2F3+%29+
Multiply the top and bottom of this fraction by +3+
+%28+3%2A7+%29+%2F+2+=+21%2F2+
+21%2F2+=+10+%2B+1%2F2+
The first part of the race was run at a rate of:
10 and 1/2 miles/hour