SOLUTION: Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 273172: Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write 2 equations:
Going to work:
d+=+r%5B1%5D%2At%5B1%5D
Coming home from work:
d+=+r%5B2%5D%2At%5B2%5D
---------------------
given:
r%5B1%5D+=+45 mi/hr
r%5B2%5D+=+30 mi/hr
t%5B1%5D+%2B+t%5B2%5D+=+1 hr
---------------------
d+=+45t%5B1%5D
d+=+30t%5B2%5D
then
d%2F45+=+t%5B1%5D
d%2F30+=+t%5B2%5D
Add the equations
d%2A%281%2F45+%2B+1%2F30%29+=+t%5B1%5D+%2B+t%5B2%5D
d+=+1%2F%281%2F45+%2B+1%2F30%29
d+=+1%2F%282%2F90+%2B+3%2F90%29
d+=+1%2F%285%2F90%29
d+=+18 mi
Esther drove 18 mi to work
check:
d%2F45+=+t%5B1%5D
t%5B1%5D+=+18%2F45
and
d%2F30+=+t%5B2%5D
t%5B2%5D+=+18%2F30
t%5B1%5D+%2B+t%5B2%5D+=+18%2F45+%2B+18%2F30
t%5B1%5D+%2B+t%5B2%5D+=+18%2A%281%2F45+%2B+1%2F30%29
t%5B1%5D+%2B+t%5B2%5D+=+18%2A%282%2F90+%2B+3%2F90%29
t%5B1%5D+%2B+t%5B2%5D+=+18%2A%285%2F90%29
t%5B1%5D+%2B+t%5B2%5D+=+18%2A%281%2F18%29
t%5B1%5D+%2B+t%5B2%5D+=+1 hr
OK