In a race from point X to point Y and back, Jack averages30mph to point Y and 10

Question

In a race from point X to point Y and back, Jack averages30mph to point Y and 10mph back to point X. Sandy averages20mph in both directions. Between Jack and Sandy, whofinished first? I think they finished at the same time (same distance, sameave speed). Am I correct? In a race from point X to point Y and back, Jack averages30mph to point Y and 10mph back to point X. Sandy averages20mph in both directions. Between Jack and Sandy, whofinished first? I think they finished at the same time (same distance, sameave speed). Am I correct?

Explanation / Answer

   Let the one side distancebe   X.    Time taken byJack   tJ   =   X/ 30   +   X /10   =   X (1/30   +   1/10)   =   4* X / 30      units    Time taken bySandy   tS   =   X/ 20   +   X /20   =   X /10   units    Clearly         tJ   <   tS    i.e. Jack finishes first.    i.e. Jack finishes first.

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