SOLUTION: Vera walked to a friends house at a rate of 3 miles per hour. Then they rode to work at a rate of 30 mph. The total time it took vera to get to work was 50 min. The total distan

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Vera walked to a friends house at a rate of 3 miles per hour. Then they rode to work at a rate of 30 mph. The total time it took vera to get to work was 50 min. The total distan      Log On

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Question 670787: Vera walked to a friends house at a rate of 3 miles per hour. Then they rode to work at a rate of 30 mph. The total time it took vera to get to work was 50 min. The total distance Vera traveled is 16 miles. How many miles did Vera walk and how many did she drive?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance that Vera walked
Let +t+ = time Vera spent walking
--------
given:
Walking:
(1) +d+=+3t+
Driving:
(2) +16+-+d+=+30%2A%28++50%2F60+-+t+%29+
-----------------------------
(2) +16+-+d+=+25+-+30t+
(2) +d+=+30t+-+9+
Substitute (1) into (2)
(2) +3t+=+30t+-+9+
(2) +27t+=+9+
(2) +t+=+1%2F3+
--------------
(1) +d+=+3%2A%281%2F3%29+
(1) +d+=+1+
+16+-+d+=+16+-+1+
+16+-+d+=+15+
----------------
She walked 1 mi and drove 15 mi
check:
(2) +16+-+d+=+30%2A%28++50%2F60+-+t+%29+
(2) +16+-+1+=+30%2A%28++5%2F6+-+1%2F3+%29+
(2) +15+=+30%2A%28+5%2F6+-+2%2F6+%29++
(2) +15+=+30%2A%281%2F2%29+
(2) +15+=+15+
OK