SOLUTION: Michael was hauling a wide load out of Portland. AT 6:00am he headed north from exit 34 at an average speed of 30mph. Ruth headed north from the same exit at 10:00am in her Pontiac

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Question 764730: Michael was hauling a wide load out of Portland. AT 6:00am he headed north from exit 34 at an average speed of 30mph. Ruth headed north from the same exit at 10:00am in her Pontiac. By 2:00pm the same day Ruth was 16 miles ahead of Micheal. What was Ruth's average speed?
Thank you for helping me solve this. I really appreciate it.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What was Michael's head start in miles?
He had a +4+ hr head start ( 6AM to 10AM )
+d%5B1%5D+=+30%2A4+
+d%5B1%5D+=+120+ miles head start
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Ruth leaves the same exit and
+4+ hrs later, ( 10AM to 2PM ), she is +16+ mi
ahead of michael
------------------
Let +d+ = distance Ruth travels from 10AM to 2 PM
+d+-+16+ = distance Michael travels from 10AM to 2 PM
Let +s+ = Ruth's average speed
------------------
Ruth's equation:
(1) +d++=+s%2A4+
Michael's equation:
(2) +%28+d+-+16+%29+-+120+=+30%2A4+
-------------------------
(2) +d+-+136+=+120+
(2) +d+=+256+
and
(1) +d+=+4s+
(1) +256+=+4s+
(1) +s+=+64+
Ruth's average speed is 64 mi/hr
check:
Michael should go +256+-+16+=+240+ mi
in +4+%2B+4++=+8+ hrs
+d%5B2%5D+=+30%2A8+
+d%5B2%5D+=+240+ mi
OK