Question 96092
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 12 miles per hour and Kate rode at 9 miles per hour. Ellen got to the library 15 minutes before Kate.
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a. how long did it take Ellen to get to the library?
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Let t = time for E to get to the library
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It says she got there 15 min ahead of K, (change 15 min to .25 hrs), therefore
(t + .25) = time for K to get to the library
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Both drove the same distance so write a distance equation:
Distance = speed * time
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E's trip = K's trip
12t = 9(t+.25)
12t = 9t + 2.25
12t - 9t = 2.25
3t = 2.25
t = 2.25/3
t = .75 hr is E's time to the library, (.75*60 = 45 min)
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b. at what time did Ellen get to the library? 
3:45 pm
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Check solution by checking the distances:
12*.75 = 9 mi
9 *(.75 + .25) = 9 mi
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