SOLUTION: At 2 p.m., two cars leave Eagle River, WI, one headed north and one headed south. If the car headed north averages 50 mph and the car headed south averages 60mph, when will the car

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Question 262836: At 2 p.m., two cars leave Eagle River, WI, one headed north and one headed south. If the car headed north averages 50 mph and the car headed south averages 60mph, when will the cars be 165 miles apart?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for each car
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D (northbound)
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D (southbound)
They both start at the same time, and I
will stop them both when they are 165 mi apart
so t%5B1%5D+=+t%5B2%5D which I'll just call t
t+=+d%5B1%5D%2Fr%5B1%5D
t+=+d%5B2%5D%2Fr%5B2%5D
Since they both equalt, I can say
d%5B1%5D%2Fr%5B1%5D+=+d%5B2%5D%2Fr%5B2%5D
Multiply both sides by r%5B1%5D%2Ar%5B2%5D
(1) d%5B1%5D%2Ar%5B2%5D+=+d%5B2%5D%2Ar%5B1%5D
I also know that
d%5B1%5D+%2B+d%5B2%5D+=+165
(2) d%5B2%5D+=+165+-+d%5B1%5D
r%5B1%5D+=+50
r%5B2%5D+=+60
(1) +60d%5B1%5D+=+50d%5B2%5D
Substituting (2) into (1)
60d%5B1%5D+=+50%2A%28165+-+d%5B1%5D%29
60d%5B1%5D+=+8250+-+50d%5B1%5D
110d%5B1%5D+=+8250
d%5B1%5D+=+75 mi
t+=+d%5B1%5D%2Fr%5B1%5D
t+=+75%2F50
t+=+1.5 hr
They will be 165 mi apart in 1.5 hr
check answer:
d%5B2%5D+=+r%5B2%5D%2At
d%5B2%5D+=+60%2A1.5
d%5B2%5D+=+90 mi
d%5B1%5D+%2B+d%5B2%5D+=+165
75+%2B+90+=+165
165+=+165
OK