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:

$speed=\frac{distance}{time}$

$time=\frac{distance}{speed}$

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,

$\frac{x}{3}+\frac{x}{7}=0.75$

Taking lcd of 7 and 3 as 21,

$\frac{7x}{21}+\frac{3x}{21}=0.75$

$\frac{10x}{21}=0.75$

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.