SOLUTION: Lisa drove 180 miles, then increased her speed by 15 miles per hour for 405 miles. If the second part of the drive took 3 hours longer than the first part, find her average speed

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Question 598388: Lisa drove 180 miles, then increased her speed by 15 miles per hour for 405 miles. If the second part of the drive took 3 hours longer than the first part, find her average speed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average speed is always ( total distance traveled ) / ( total time )
Lisa's total distance traveled is +180+%2B+405+=+585+
Let +t+ = Lisa's time for 1st part in hours
Lisa's speed for the 1st part is +180+%2F+t+
Lisa's speed for the 2nd part is +180+%2F+t+%2B+15+
Lisa's time for the 2nd part is +t+%2B+3+, so
+180%2Ft+%2B+15+=+405+%2F+%28+t+%2B+3+%29+
Multiply both sides by +t%2A%28+t+%2B+3+%29+
+180%2A%28+t+%2B+3+%29+%2B+15%2At%2A%28+t+%2B+3+%29+=+405t+
+180t+%2B+540+%2B+15t%5E2+%2B+45t+=+405t+
+15t%5E2+%2B+225t+-+405t+%2B+540+=+0+
+15t%5E2+-+180t++%2B+540+=+0+
+t%5E2+-+12t+%2B+36+=+0+
By the quadratic formula:
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-12+
+c+=+36+
+t+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A36+%29%29+%2F+%282%2A1%29+
+t+=+%28+12+%2B-+sqrt%28+144+-+144+%29%29+%2F+2+
+t+=+%28+12+%2F+2+%29+
+t+=+6+
+t+%2B+3+=+9+
+9+%2B+6+=+15+
Lisa's average speed was +585+%2F+15+=+39+
39 mi/hr