Q:

Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

Accepted Solution

A:
Answer:The distance between the two cities isd= 838.1mStep-by-step explanation:d= distance between the two cities [tex]v=\frac{x}{t}[/tex]The time of the all travel is 32 hrs[tex]t_{1}+t_{2}=32hrs[/tex][tex]t=\frac{x}{v}[/tex][tex]t_{1}=\frac{d}{v_{1}}[/tex][tex]t_{2}=\frac{d}{v_{2}}[/tex][tex]\frac{d}{v_{1}}+\frac{d}{v_{2}}=32[/tex][tex]\frac{d}{55}+\frac{d}{50}=32[/tex]Resolving to d [tex]d*21=550*32[/tex][tex]d=\frac{17600}{21}[/tex][tex]d=838.1 miles[/tex]Check:[tex]\frac{d}{v_{1}}+\frac{d}{v_{2}}=32[/tex][tex]\frac{838.1}{50}+\frac{838.1}{55}=32[/tex][tex]32=32[/tex]