Let us say distance between Eugenia's home and school is x miles.
Speed of Eugenia when she walked from home to school = 3 mph
Speed of Eugenia when she walked from school to home = 7 mph
Total time taken = 45 minutes or 0.75 hours
We know that the speed distance formula is given by:
[tex]speed=\frac{distance}{time}[/tex]
[tex]time=\frac{distance}{speed}[/tex]
Time taken by Eugenia when she walked from home to school = x/3 hours
Time taken by Eugenia when she walked from school to home = x/7 hours
Total time taken = x/3+x/7
So forming an equation we have,
[tex]\frac{x}{3}+\frac{x}{7}=0.75[/tex]
Taking lcd of 7 and 3 as 21,
[tex]\frac{7x}{21}+\frac{3x}{21}=0.75[/tex]
[tex]\frac{10x}{21}=0.75[/tex]
10x=15.75
Dividing both sides by 10 , we have
x= 1.575
Answer: So we can say that the distance between Eugenia's house and school is 1.575 miles.
