SOLUTION: when blake drives to work on the highway, he averages 45mph. when he uses the local roads he averages 36mph. the trip on the local roads is 3 mi shorter and takes 5 more minutes th

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Question 893133: when blake drives to work on the highway, he averages 45mph. when he uses the local roads he averages 36mph. the trip on the local roads is 3 mi shorter and takes 5 more minutes than the highway trip. how many miles long is the highway trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in miles he drives on highway
Let +t+ = time in hours he spends on highway
--------------------------------------------
Now convert +5+ minutes to hours
( minutes ) x ( hours / minute )
+5%2A%28+1%2F60+%29++=+1%2F12+ hrs
--------------------------
Equation for driving on highway:
(1) +d+=+45t+
Equation for driving on local roads:
(2) +d+-+3+=+36%2A%28+t+%2B+1%2F12+%29+
(2) +d+=+36t+%2B+3+%2B+3+
(2) +d+=+36t+%2B+6+
--------------------
Substitute (1) into (2)
(2) +45t+=+36t+%2B+6+
(2) +9t+=+6+
(2) +t+=+2%2F3+ hrs
and, since
(1) +d+=+45t+
(1) +d+=+45%2A%282%2F3%29+
(1) +d+=+30+
He drove 30 highway miles
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check:
(2) +d+-+3+=+36%2A%28+t+%2B+1%2F12+%29+
(2) +30+-+3+=+36%2A%28+2%2F3+%2B+1%2F12+%29+
(2) +27+=+36%2A%28+8%2F12+%2B+1%2F12+%29+
(2) +27+=+36%2A%28+9%2F12+%29+
(2) +27+=+3%2A9+
(2) +27+=+27+
OK