SOLUTION: Chris traveled 1 hour longer and 2 miles farther than Calvin, but averaged 3 mph slower. If the sum of their times was 4 hours, what was the sum in miles of the distances they tra

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Question 734161: Chris traveled 1 hour longer and 2 miles farther than Calvin, but averaged 3 mph slower.
If the sum of their times was 4 hours, what was the sum in miles of the distances they traveled?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = Calvin's distance in miles
Let +t+ = Calvin's time in hrs
Let +s+ = Calvin's speed in mi/hr
------------------------
Calvin's equation:
(1) +d+=+s%2At+
Chris's equation:
(2) +d+%2B+2+=+%28+s+-+3+%29%2A%28+t+%2B+1+%29+
----------------------------
given:
+t+%2B+t+%2B+1+=+4+
+2t+=+3+
+t+=+1.5+
Substitute (1) into (2)
(2) +s%2At+%2B+2+=+%28+s+-+3+%29%2A%28+t+%2B+1+%29+
(2) +s%2At+%2B+2+=+s%2At+-+3t+%2B+s+-+3+%7D%7D%0D%0A%282%29+%7B%7B%7B+2+=+-3t+%2B+s+-+3+
(2) +3t+=+s+-+5+
(2) +3%2A1.5+=+s+-+5+
(2) +s+=+9.5+
and
(1) +d+=+s%2At+
(1) +d+=+9.5%2A1.5+
(1) +d+=+14.25+
+d+%2B+2+=+14.25+%2B+2+
+d+%2B+2+=+16.25+
The sum of their distances is
+d+%2B+d+%2B+2+=+14.25+%2B+16.25+
+2d+%2B+2+=+30.5+ miles
check:
(2) +d+%2B+2+=+%28+s+-+3+%29%2A%28+t+%2B+1+%29+
(2) +d+%2B+2+=+%28+9.5+-+3+%29%2A%28+1.5+%2B+1+%29+
(2) +d+%2B+2+=+6.5%2A2.5+
(2) +d+%2B+2+=+16.25+
OK