Question

Eugenia walked all the way to school at 3 mph then realized she forgot her math book (how could she?!), so she ran back at 7 mph. If she got back to her house 45 minutes after she left, how far does she live from school?

Answer 1

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:

`speed=(distance)/(time)`

`time=(distance)/(speed)`

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,

`(x)/(3)+(x)/(7)=0.75`

Taking lcd of 7 and 3 as 21,

`(7x)/(21)+(3x)/(21)=0.75`

`(10x)/(21)=0.75`

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.