Hello, Jerry!
Bob and Carol moved to Bainbridge.
Carol drove for ten hours at \(\displaystyle x\) miles per hour.
Bob drove at 10 mph slower than Carol; his trip took 15 hours.
How far away did they live from Bainbridge?
Carol drove for 10 hours at \(\displaystyle x\) mph . . . She drove \(\displaystyle 10x\) miles.
Bob drove for 15 hours at \(\displaystyle x-10\) mph . . . He drove \(\displaystyle 15(x-10)\) miles.
Since they drove the same distance: \(\displaystyle \:10x\:=\:15(x\,-\,10)\)
Solve for \(\displaystyle x\) and we get: \(\displaystyle x\,=\,30\) . . . That's Carol's speed.
Since she drove at that speed for 10 hours, her distance was: \(\displaystyle \,10\,\times30\:=\:300\) miles.
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Check
Bob drove 10 mph slower . . . at 20 mph.
He drove 15 hours at 20 mph . . . His distance was: \(\displaystyle \.15\,\times 20\:=\;300\) miles.
\(\displaystyle \;\;\)
Check!