SOLUTION: Ellen and Kate raced on their bike to the library after school. They both left school at 3p.m. and biked along the same path. Ellen rode at a speed of 12 mph and Kate rode at a spe

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Ellen and Kate raced on their bike to the library after school. They both left school at 3p.m. and biked along the same path. Ellen rode at a speed of 12 mph and Kate rode at a spe      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 112834: Ellen and Kate raced on their bike to the library after school. They both left school at 3p.m. and biked along the same path. Ellen rode at a speed of 12 mph and Kate rode at a speed of 9 mph. Ellen got to the library 15 minutes before Kate. How long did it take Ellen to get to the library and what time did Ellen get to the library.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Ellen and Kate raced on their bike to the library after school. They both left school at 3p.m. and biked along the same path. Ellen rode at a speed of 12 mph and Kate rode at a speed of 9 mph. Ellen got to the library 15 minutes before Kate. How long did it take Ellen to get to the library and what time did Ellen get to the library.
:
Let t = time required (in hrs) for E to get to the library
Then
(t + .25) = time required for K to get to the library (changed 15 min to hrs)
:
We know they both traveled the same distance. Make a distance equation
Dist = speed * time
:
E's dist = K's dist
12t = 9(t + .25)
12t = 9t + 2.25
12t - 9t = 2.25
3t = 2.25
t = 2.25/3
t = .75 hr or 45 min
:
E got to the library at 3:45
:
:
Confirm out solution by finding that they did, in fact, travel the same distance
K's time .75 + .25 = 1 hr
9 * 1 = 9 mi
12 * .75 = 9 mi
;
Did this make sense to you? Any questions?