SOLUTION: hey i need help on this one here would really appreciate it... Harriet drove for 90 miles in the city. when she got on the highway she increased her speed by 20 mph and drove fo

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Question 682925: hey i need help on this one here would really appreciate it...
Harriet drove for 90 miles in the city. when she got on the highway she increased her speed by 20 mph and drove for 130 miles. If Harriet drove for a total of 4 hours, how fast did she drive on the highway?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed in mi/hr in the city
+s+%2B+20+ = her speed in mi/hr on the highway
Let +t+ = time in hrs she drove in the city
+4+-+t+ = time in hrs she drove on the highway
---------------
Harriet's equation for the city:
(1) +90+=+s%2At+
Harriet's equation for the highway:
(2) +130+=+%28+s+%2B+20+%29%2A%28+4+-+t+%29+
----------------------------
(1) +t+=+90%2Fs+
and
(2) +130+=+4s+%2B+80+-+s%2At+-+20t+
(2) +130+=+4s+%2B+80+-+s%2A%28+90%2Fs+%29+-+20%2A%28+90%2Fs+%29+
(2) +130+=+4s+%2B+80+-+90+-+1800%2Fs+
(2) +130s+=+4s%5E2+-+10s+-+1800+
(2) +4s%5E2+-+140s+-+1800+=+0+
(2) +s%5E2+-+35s+-+450+=+0+
Use the quadratic formula
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-35+
+c+=+-450+
+s+=+%28+-%28-35%29+%2B-+sqrt%28+%28-35%29%5E2+-+4%2A1%2A%28-450%29+%29%29+%2F+%282%2A1%29+
+s+=+%28+35+%2B-+sqrt%28+1225+%2B+1800+%29%29+%2F+2+
+s+=+%28+35+%2B-+sqrt%28+3025+%29%29+%2F+2+
+s+=+%28+35+%2B+55+%29+%2F+2+
+s+=+90%2F2+
+s+=+45+
and, since +s+%2B+20+ = her speed on the highway,
+s+%2B+20+=+45+%2B+20+
+s+%2B+20+=+65+
She drove 65 mi/hr on the highway
check:
(2) +130+=+%28+s+%2B+20+%29%2A%28+4+-+t+%29+
(2) +130+=+%28+45+%2B+20+%29%2A%28+4+-+t+%29+
(2) +130+=+65%2A%28+4+-+t+%29+
(2) +130+=+260+-+65t+
(2) +65t+=+130+
(2) +t+=+2+ hrs
and
(1) +t+=+90%2Fs+
(1) +t+=+90%2F45+
(1) +t+=+2+ hrs
OK