SOLUTION: Landon can climb a hill at a rate that is 2.5 mph slower than his rate coming down the hill. If it takes him 6 hours to climb the hill and 135 minutes to come down the hill what is

Algebra ->  Finance -> SOLUTION: Landon can climb a hill at a rate that is 2.5 mph slower than his rate coming down the hill. If it takes him 6 hours to climb the hill and 135 minutes to come down the hill what is      Log On


   

Question 1070756: Landon can climb a hill at a rate that is 2.5 mph slower than his rate coming down the hill. If it takes him 6 hours to climb the hill and 135 minutes to come down the hill what is his rate coming down?
Thank you for the help!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert 135 min to hrs:
+135%2A%28+1%2F60+%29+=+2.25+
Let +d+ = the one-way distance up the hill
Let +s+ = his rate coming down the hill
+s+-+2.5+ = his rate going up the hill
--------------------------------------------
Going up the hill:
(1) +d+=+%28+s+-+2.5+%29%2A6+
Going down the hill:
(2) +d+=+s%2A2.25+
------------------------
Substitute (2) into (1)
(1) +s%2A2.25+=+%28+s+-+2.5+%29%2A6+
(1) +2.25s+=+6s+-+15+
(1) +3.75s+=+15+
(1) +s+=+4+
------------------------
His rate coming down the hill is 4 mi/hr
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check:
(2) +d+=+s%2A2.25+
(2) +d+=+4%2A2.25+
(2) +d+=+9+ mi
and
(1) +d+=+%28+s+-+2.5+%29%2A6+
(1) +d+=+%28+4+-+2.5+%29%2A6+
(1) +d+=+1.5%2A6+
(1) +d+=+9+ mi
OK