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Which is better in the following sentences, “zoom his way” or “zoom their ways”?

which is wrong in the following sentences, “zoom his way” or “zoom their ways”?

…Soon the world would hear of Zewail’s award --- the 1999 Nobel Prize in chemistry --- and Zewail would hear from the world. Two thousand e-mails would zoom his way within a few days and three phone lines would start ringing with eager requests for interviews from the international and Egyptian press and with congratulations from friends and colleagues…

…Soon the world would hear of Zewail’s award --- the 1999 Nobel Prize in chemistry --- and Zewail would hear from the world. Two thousand e-mails would zoom their ways within a few days and three phone lines would start ringing with eager requests for interviews from the international and Egyptian press and with congratulations from friends and colleagues…

Thank you very much!
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...Soon the world would hear of Zewail's award --- the 1999 Nobel Prize in chemistry --- and Zewail would hear from the world. Two thousand e-mails would zoom his way within a few days and three phone lines would start ringing with eager requests for interviews from the international and Egyptian press and with congratulations from friends and colleagues...

is correct.
Comments  
His
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The answer "His" is for the first question or for the second question?

Thank you very much!
Allow me clarify my questions:

1. Which is better in the following sentences, “zoom his way” or “zoom their ways”?

2. which is wrong in the following sentences, “zoom his way” or “zoom their ways”?

3. What/who does the dependent possessive pronoun (their/his/its, whatever it could be) which is immediately behind the word “zoom” refer to?

…Soon the world would hear of Zewail’s award --- the 1999 Nobel Prize in chemistry --- and Zewail would hear from the world. Two thousand e-mails would zoom his way within a few days and three phone lines would start ringing with eager requests for interviews from the international and Egyptian press and with congratulations from friends and colleagues…

…Soon the world would hear of Zewail’s award --- the 1999 Nobel Prize in chemistry --- and Zewail would hear from the world. Two thousand e-mails would zoom their ways within a few days and three phone lines would start ringing with eager requests for interviews from the international and Egyptian press and with congratulations from friends and colleagues…

Thank you very much!
Your help would be appreciated
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 anonymous's reply was promoted to an answer.
So the "his" refers to Zewail? But one thing which bothers me is that the subject of the verb "zoom" is the "two thousand e-mails" not Zewail.

Thank you very much!