A critical examination of this passage in the Hebrew language in which the Old Testament was written discloses the fact that Joshua never requested the Lord to cause the sun and moon to stand still. His request was that the sunlight and the moonlight might be restrained or prevented from shining through the dark clouds of the storm mentioned in verse 11, in which great hailstones had been formed, and doubtless were accompanied by thunder and lightning, all of which would strike terror into the hearts of the Amorites. Had the dark clouds rolled away and the sun shone forth, the enemies of Israel (who were sun worshippers) would have been courageous and resisted the onslaughts of Joshua and his army. So, the sunlight and the moonlight remained dim (Hebrew) about a whole day, “until the people had avenged themselves upon their enemies.” The scientists are right and in harmony with the Scriptures, as the earth did not cease to revolve upon its axis. The Bible rightly interpreted and understood is consistent with reason and with facts.

Additional Resources:  

Beauties of the Truth (quarterly publication): “Joshua’s Request”

Christian Questions Podcast 
Episode #1220: “Can Faith Take Me From Failure to Victory?”
Powerful lessons of faith overcoming adversity from the life of Joshua
Preview Video  
CQ Rewind Show Notes