Answer:
Sandy will finish the race first.
Step-by-step explanation:
Let D be the total one sided distance in miles, ( between X and Y ),
We know that,
[tex]Speed =\frac{Distance}{Time}[/tex]
[tex]\implies Time =\frac{Distance}{Speed}[/tex]
Since, from point X to point Y and back, Jack averages 30 miles per hour to point Y and 10 miles per hour back to point X.
So, the total time taken by Jack = [tex]\frac{D}{30}+\frac{D}{10}[/tex]
[tex]=\frac{D+3D}{30}[/tex]
[tex]=\frac{4D}{30}[/tex]
[tex]=0.1333D[/tex]
Also, Sandy averages 20 miles per hour in both directions,
So, the total time taken by Sandy = [tex]\frac{D}{20}+\frac{D}{20}[/tex]
[tex]=\frac{D+D}{20}[/tex]
[tex]=\frac{2D}{20}[/tex]
[tex]=\frac{D}{10}[/tex]
[tex]=0.10D[/tex]
∵ 0.133D > 0.10D
Hence, Sandy will finish the race first.
