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I need help with this question Ellen and Kate raced on their bikes to the library after school. They both left school at 3:00pm. and bicycled along the same path and Ellen rode at a speed of 12 miles per hour and Kate rode at a speed of 9 hours per hour. Ellen got to the library 15 minutes before Kate. What time did Ellen get to the library?

Mathematics
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Used these steps 1) define the variables 2) relate the problem to some previous formula or information you have learned. 3) Write an equation based on the equation and answer the question that was asked. 5) check your answer, I would like to have a decent conversation in how to answer this question I will be appreciated.
d = v * t 12t = 9 ( t + 1/4 )
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Other answers:

Let t is the time in hour Ellen rode to the library -> t + 1/4 is the time Kate rode to the library Since the distance equal d1 = d2 <=> v1 t = v2 ( t + 1/4)
thank you
how would i check it
the answer
Just plug the answer to see if the distances are equal !
ok
thanks

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