SOLUTION: Lisa drove 60 miles, then increased her speed by 15 miles per hour for 135 miles. If the second part of the drive took 1 hour longer than the first part, find her average speed

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Question 1086507: Lisa drove 60 miles, then increased her speed by 15 miles per hour for 135 miles. If the second part of the drive took 1 hour 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!
Note that average speed is always:
[ total distance ] / [ total time ]
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Let +t+ = her time in hrs for the 1st part of the trip
+d+=+r%2At+
(1) +60+=+r%2At+
(1) +r+=+60%2Ft+
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For the 2nd part:
(2) +135=+%28+r+%2B+15+%29%2A%28+t%2B1+%29+
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Plug (1) into (2)
(2) +135+=+%28+60%2Ft+%2B+15+%29%2A%28+t+%2B+1+%29+
(2) +135+=+60+%2B+15t+%2B+60%2Ft+%2B+15+
(2) +60%2Ft+=+60+-+15t+
(2) +60+=+60t+-+15t%5E2+
(2) +t%5E2+-+4t+%2B+4+=+0+
(2) +%28+t+-+2+%29%5E2+=+0+
(2) +t+=+2+
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Her total time was:
+t+%2B+%28+t%2B1+%29+=+2t+%2B+1+
+2t+%2B+1+=+2%2A2+%2B+1+
+2t+%2B+1+=+5+ hrs
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Her total distance was:
+60+%2B+135+=+195+
and
Ave speed = +195%2F5+=+39+
39 mi/hr
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check the math & get a 2nd opinion if needed