SOLUTION: A tour bus leaves Sacramento every Friday evening at 5:00 PM, for a 270-mile trip to Las Vegas. This week, however, the bus leaves at 5:30PM. To arrive in Las Vegas on time, the dr

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A tour bus leaves Sacramento every Friday evening at 5:00 PM, for a 270-mile trip to Las Vegas. This week, however, the bus leaves at 5:30PM. To arrive in Las Vegas on time, the dr      Log On

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Question 903851: A tour bus leaves Sacramento every Friday evening at 5:00 PM, for a 270-mile trip to Las Vegas. This week, however, the bus leaves at 5:30PM. To arrive in Las Vegas on time, the driver drives 5 miles per hour faster than usual. At what speed does she usually drive?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the bus's normal time
in hrs to make the trip
+270%2Ft+ = the bus's normal speed
---------------------------------
+270+=+%28+270%2Ft+%2B+5+%29%2A%28+t+-+.5+%29+
+270+=+270+%2B+5t+-+135%2Ft+-+2.5+
+0+=+5t+-+135%2Ft+-+2.5+
+5t+-+2.5+-+135%2Ft+=+0+
+5t%5E2+-+2.5t+-+135+=+0+
+50t%5E2+-+25t+-+1350+=+0+
+2t%5E2+-+t+-+54+=+0+
----------------------
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-1+
+c+=+-54+
+t+=+%28+-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A2%2A%28-54%29+%29%29+%2F+%282%2A2%29+
+t+=+%28+1+%2B-+sqrt%28+1+%2B+432+%29%29+%2F+4+
+t+=+%28+1+%2B-+sqrt%28+433+%29%29+%2F+4+
+t+=+%28+1+%2B+20.809+%29+%2F+4+
+t+=+21.809+%2F+4+
+t+=+5.452+
+270%2Ft+ = the bus's normal speed
+270%2F5.452+=+49.523+
The bus's normal speed was 49.523 mi/hr
------------
check:
+270+=+%28+270%2Ft+%2B+5+%29%2A%28+t+-+.5+%29+
+270+=+%28+270%2F5.452+%2B+5+%29%2A%28+5.452+-+.5+%29+
+270+=+%28+49.523+%2B+5+%29%2A4.952+
+270+=+54.523%2A4.952+
+270+=+269.9998+
close enough
Hope I got it