let

v = the rate of Sue, v>0

Sue travels 13 miles per hour faster than Doreen:

v - 13 = the rate of Doreen

since time = distance/time

120/v = the time of Sue riding moped for 120 mi

56/(v - 13) = the time of Doreen riding a bicycle for 56 mi

To travel 120 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 56 miles riding a bicycle we have:

120/v = 56/(v - 13) - 2

by solving the equation we find:

v = 20 mph the rate of Sue

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v - 13 = 20 - 13 = 7 mph the rate of Doreen

120/v = 120/20 = 6 hr the time of Sue riding moped for 120 mi

56/(v - 13) = 56/7 = 8 hr the time of Doreen riding a bicycle for 56 mi

Sue's rate is 20 mph and her time is 6 hours.

Doreen's rate is 7 mph and her time is 8 hours.