Answer:
The distance between the two cities is
d= 838.1m
Step-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]
