SOLUTION: Jamie recently drove to visit her parents who live 870 miles away. On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weath

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Question 1054727: Jamie recently drove to visit her parents who live 870 miles away. On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of 29 hours driving, find the two rates.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed driving back home in mi/hr
+s+%2B+25+ = her speed driving to parents in mi/hr
Let +t+ = her time in hrs to drive back home
+29+-+t+ = her time driving to parents house in hrs
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Driving to parents house:
(1) +870+=+%28+s%2B25+%29%2A%28+29+-+t+%29+
Driving back home:
(2) +870+=+s%2At+
-------------------------------
(2) +t+=+870%2Fs+
Plug (2) into (1)
(1) +870+=+%28+s%2B25+%29%2A%28+29+-+870%2Fs+%29+
(1) +870+=+29s+%2B+725+-+870+-+21750%2Fs+
(1) +1740+-+725+=+29s+-+21750%2Fs+
(1) +1015+=+29s+-+21750%2Fs+
(1) +1015s+=+29s%5E2+-+21750+
(1) +29s%5E2+-+1015s+-+21750+=+0+
(1) +s%5E2+-+35s+-+750+=+0+
(1) +%28+s+-+50+%29%2A%28+s+%2B+15+%29+=+0+ ( by looking at this )
+s+=+50+ ( because the speed must be positive )
and
+s+%2B+25+=+75+
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Her speed driving back home in mi/hr is 50 mi/hr
Her speed driving to parents in mi/hr is 75 mi/hr
------------------------------------------------
check:
(2) +870+=+s%2At+
(2) +870+=+50t+
(2) +t+=+17.4+ hrs
and
(1) +870+=+%28+50%2B25+%29%2A%28+29+-+t+%29+
(1) +870+=+75%2A%28+29+-+t+%29+
(1) +870+=+2175+-+75t+
(1) +75t+=+1305+
(1) +t+=+17.4+ hrs
OK