SOLUTION: If you travel 180 miles and then travel 15 Mph faster and get there an hour sooner how fast we're u going

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Question 698181: If you travel 180 miles and then travel 15 Mph faster and get there an hour sooner how fast we're u going
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+d+=+r%2At+
given:
+d+=+180+ mi
Let +r+ = usual rate
Let +t+ = time to go 180 mi at usual rate
+r+%2B+15+ = faster rate
+t+-+1+ = time to go 180 mi at faster rate
--------------
At usual rate:
(1) +180+=+r%2At+
At faster rate:
(2) +180+=+%28+r+%2B+15+%29%2A%28+t+-+1+%29+
----------------------------
(2) +180+=+r%2At+%2B+15t+-+r+-+15+
and
(1) +t+=+180%2Fr+
Substitute this into (2)
(2) +180+=+r%2A%28180%2Fr%29+%2B+15%2A%28180%2Fr%29+-+r+-+15+
(2) +15%2A%28180%2Fr%29+-+r+=+15+
Multiply both sides by +r+
(2) +2700++-+r%5E2+=+15r+
(2) +r%5E2+%2B+15r+-+2700+=+0+
Use quadratic formula
+r+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+15+
+c+=+-2700+
+r+=+%28+-15+%2B-+sqrt%28+15%5E2+-+4%2A1%2A%28-2700%29+%29%29+%2F+%282%2A1%29+
+r+=+%28+-15+%2B-+sqrt%28+225+%2B+10800+%29%29+%2F+2+
+r+=+%28+-15+%2B-+sqrt%28+11025+%29%29+%2F+2+
+r+=+%28+-15+%2B+105%29+%2F+2+
+r+=+90%2F2+
+r+=+45+
+r+%2B+15+=+60+
Your usual speed is 45 mi/hr
Your faster speed is 60 mi/hr
check answer:
(1) +t+=+180%2Fr+
(1) +t+=+180%2F45+
(1) +t+=+4+ hrs
and
(2) +180+=+%28+45+%2B+15+%29%2A%28+4+-+1+%29+
(2) +180+=+60%2A3+
(20 +180+=+180+
OK