SOLUTION: Ellen and Kate raced on their bicycles to the library after school. They both left school at 3:00pm and bicycled along the same path. Ellen rode at a speed of 12mph and Kate rode a

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Question 423139: Ellen and Kate raced on their bicycles to the library after school. They both left school at 3:00pm and bicycled along the same path. Ellen rode at a speed of 12mph and Kate rode at a speed of 9mph. Ellen got to the library 15mins before Kate. What time did Ellen get to the library?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Ellen and Kate raced on their bicycles to the library after school.
They both left school at 3:00pm and bicycled along the same path.
Ellen rode at a speed of 12mph and Kate rode at a speed of 9mph.
Ellen got to the library 15mins before Kate.
What time did Ellen get to the library?
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Ellen data:
rate = 12 mph ; time = x hrs. ; distance = rt = 12x miles
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Kate data:
rate = 9 mph ; time = (x+(1/4)) hrs ; distance = 9(x+(1/4)) = 9x+(9/4) miles
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Equation:
12x = 9x+(9/4)
3x = 9/4
x = 3/4 hr.
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Ellen will arrive at the library at 3:45
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Ellen's equation:

Kate's equation:

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By substitution:

Ellen got to the library in .75 hrs or 45 min
check answer:

and

OK