"Henrietta drove from her home to Boston and back again along the same road in a total of 10 hours. Her average rate going was 20 mph while her average rate on the return trip was 30 mph. How long did she take in each direction, and what distance did she cover each way?"

Time ratio of depart:return is 3:2 because it is directly proportional to the mph rate she was going.

Using that ratio,
2x+3x=10, 5x=10, x=2.. we know she spent 4 hours going and 6 returning.

six hours at 20mph gives us 20*6=120 miles.

four hours (should give us the same) at 30 mph gives us 30*4=120 miles

they are indeed the same.

She took six hours going and four returning, and went 120 miles on each voyage, giving us a total of 240 miles.