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 12 miles per hour and

Question 96092This question is from textbook prentice hall mathematics algebra 1
: 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.

a. how long did it take ellen to get to the library?
b. at what time did ellen get to the library?
Could someone please explain this problem to me in depth?...( step by step)
Thanks! This question is from textbook prentice hall mathematics algebra 1

Answer by ankor@dixie-net.com(22740) (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 12 miles per hour and Kate rode at 9 miles per hour. Ellen got to the library 15 minutes before Kate.
:
a. how long did it take Ellen to get to the library?
:
Let t = time for E to get to the library
:
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
:
Both drove the same distance so write a distance equation:
Distance = speed * time
:
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)
:
b. at what time did Ellen get to the library?
3:45 pm
:
:
Check solution by checking the distances:
12*.75 = 9 mi
9 *(.75 + .25) = 9 mi
:
Was this step-by-step enough for you? Any questions?
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