SOLUTION: Esther drove to work in the morning at an average speed of 45mph. She returned home in the evening along the same and averaged 30mph. If Esther spent a total of one hour commutin

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Question 198831This question is from textbook
: Esther drove to work in the morning at an average speed of 45mph. She returned home in the evening along the same and averaged 30mph. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning? This question is from textbook

Found 2 solutions by arallie, jojo14344:
Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
Here we go
If45x=30y and x%2By=60 where x=time to work and y=time to house
Then 45%2860-y%29=30y
Solve for y
2700-45y=30y
75y=2700
36=y
If x%2By=60 when y=36
Then x=24
If45x%2F60=30y%2F60=d where d=distance and 60=minutes in an hour.
Then45%2824%29%2F60=30%2836%29%2F60=d
Solve for d
1080%2F60=1080%2F60=d
18=18=d
18mi
Anymore questions feel free to ask me.
Anthony Allie
arallie@gmail.com
http://arallie.webs.com/tutoring.htm

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Going Work in the morning:
Speed=S%5BW%5D=45mph & time=t

Going home:
Speed=S%5BH%5D=30mph & time=%281hr-t%29


Distance Formula : D = Speed x time

D%5BW%5D=S%5BW%5Dt
D%5BH%5D=S%5BH%5D%281-t%29

Since Distance is the same, we can equate the two:
D%5BW%5D=D%5BH%5D
S%5BW%5Dt=S%5BH%5D%281-t%29
%2845%29%28t%29=%2830%29%281-t%29
45t=30-30t ----> 45t%2B30t=30 ---> 75t=30 ---> cross%2875%29t%2Fcross%2875%29=cross%2830%290.40%2Fcross%2875%29}
red%28t=0.40hr%29 x %2860min%2F1cross%28hr%29%29 = red%2824mins%29

So the Distance, D%5BW%5D=S%5BW%5Dt=%2845%29%280.40%29=red%2818miles%29,( Answer )

To check, the Distance going home should be the same.
D%5BH%5D=S%5BH%5D%281-t%29
D%5BH%5D=%2830%29%281-0.40%29=%2830%29highlight%280.60%29=red%2818miles%29, oks!

Total time spent driving:
time(Work) + time(Home) = 1 hour
0.40%2Bhighlight%280.60%29=1hr
1hr=1hr

Thank you,
Jojo