Tom and Sarah start a journey from the same point to a destination. Tom travels at an average speed of 60 miles per hour, while Sarah travels at an average speed of 70 miles per hour. After reaching the destination, they immediately return using the same route. Tom increases his speed by 20% on the return journey compared to his outbound journey, and Sarah maintains her original speed. What is the absolute difference between Tom's and Sarah's average speeds (in miles per hour) for the entire round trip?

Assume the destination is 420 miles away. Tom takes 7 hours to drive there at 60 mph and returns at 72 mph (a 20% increase), taking 420 divided by 72, which equals 35/6 hours. Tom's average speed for the round trip is calculated as total distance divided by total time: 840 divided by (42/6 + 35/6) equals 840 multiplied by 6/77, resulting in 720/11 mph. Sarah takes 6 hours to go there at 70 mph and 6 hours to return at 70 mph, so her average speed is 70 mph. The absolute difference between their average speeds is 70 minus 720/11, which equals (770 minus 720) / 11, resulting in 50/11 miles per hour.

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