Let x represent the distance on her way to her friend's house and also the distance travelled on returning
Time = distance/speed
The rate or speed at which Amy dove to her friend's house is 45mph
Time spent in travelling to her friend's house is x/45
The rate or speed at which Amy returned from her friend's house is 50mph
Time spent in travelling returning from her friend's house is x/50
The time for the round trip is the total time spent in going and returning. This means that
[tex]\begin{gathered} \frac{x}{45}\text{ + }\frac{x}{50\text{ }}\text{ = 4} \\ \text{Multiplying both sides of the equation by 2250, it becomes} \\ 50x\text{ + 45x = 9000} \\ 95x\text{ = 9000} \\ x\text{ = }\frac{9000}{95} \\ x\text{ = 95} \\ \text{The total distance is } \\ 95\text{ }\times2\text{ = 190 miles} \end{gathered}[/tex]