SOLUTION: A biker bikes 2.7 hours to the city. Bikerbikes .9 hrs more coming back at 3 miles per hours slower. What is the total distance biker biked?

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Question 473957: A biker bikes 2.7 hours to the city. Bikerbikes .9 hrs more coming back at 3 miles per hours slower. What is the total distance biker biked?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = biker's speed going to city
given:
Time going to city is +t+=+2.7+ hrs
+d+=+s%2At+
+d+=+s%2A2.7+
---------------
Coming back from city is the same distance, so
+d+=+%28+s+-+3%29%2A%282.7+%2B+.9%29+
+d+=+2.7s+-+8.1+%2B+.9s+-+2.7+
+d+=+3.6s+-+10.8+
---------------
Since the distances are equal,
+s%2A2.7+=+3.6s+-+10.8+
Subtract +2.7s+ from both sides
+0+=+.9s+-+10.8+
Add +10.8+ to both sides
+.9s+=+10.8+
+s+=+12+
--------------
Now find +d+
+d+=+2.7s+
+d+=+2.7%2A12+
+d+=+32.4+
--------------
Since the biker went to the city and
then back again, you need to find +2d+
+2d+=+2%2A32.4+
+2d+=+64.8+
The total distance biked is 64.8 mi
check:
+d+=+%28+s+-+3%29%2A%282.7+%2B+.9%29+
+d+=+%28+12+-+3%29%2A%282.7+%2B+.9%29+
+d+=+9%2A3.6+
+d+=+32.4+
+2d+=+64.8+
OK