SOLUTION: Jessie recently drove to visit her parents who live 540 miles away. On her way there her average speed was 9 miles per hour faster than on her way home (she ran into some bad weath

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Jessie recently drove to visit her parents who live 540 miles away. On her way there her average speed was 9 miles per hour faster than on her way home (she ran into some bad weath      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 963356: Jessie recently drove to visit her parents who live 540 miles away. On her way there her average speed was 9 miles per hour faster than on her way home (she ran into some bad weather). If Jessie spent a total of 27 hours driving, find the two rates.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The distance is the same.
R%5B1%5D%2At%5B1%5D=540
R%5B2%5D%2At%5B2%5D=540
.
.
R%5B1%5D=9%2BR%5B2%5D%2B9
.
.
t%5B1%5D%2Bt%5B2%5D=27
540%2FR%5B1%5D%2B540%2FR%5B2%5D=27
540%2F%28R%5B2%5D%2B9%29%2B540%2FR%5B2%5D=27
540R%5B2%5D%2B540%2A%289%2BR%5B2%5D%29=27R%5B2%5D%289%2BR%5B2%5D%29
540R%5B2%5D%2B4860%2B540R%5B2%5D=243R%5B2%5D%2B27R%5B2%5D%5E2
1080R%5B2%5D%2B4860=243R%5B2%5D%2B27R%5B2%5D%5E2
27R%5B2%5D%5E2-837R%5B2%5D-4860=0
27R%5B2%5D%5E2-837R%5B2%5D-4860=0
R%5B2%5D%5E2-31R%5B2%5D-180=0
%28R%5B2%5D-36%29%28R%5B2%5D%2B5%29=0
Only the positive solution makes sense in this problem.
R%5B2%5D-36=0
R%5B2%5D=36mph
Then,
R%5B1%5D=36%2B9
R%5B1%5D=45mph
and,
t%5B1%5D=540%2F45
t%5B1%5D=12hr
and,
t%5B2%5D=540%2F36
t%5B2%5D=15hr