To travel 105 miles, it takes sue, riding a moped, 3 hours less time than it takes doreen to travel 64 miles riding a bicycle. sue travels 13 miles per hour faster than doreen. find the times and rates of both girls.

Let t=time Doreen travels; let r=rate of Doreen

                RATE * TIME = DIST.
        Sue | r+13      t-3       105
   Doreen |   r           t          64
 
Now solve the system:
(r+13)(t-3)=105
r*t=64
 

             
Doreen: rate = 8 mph, time = 8 hours
Sue:  rate = 21 mph, time = 5 hours

Step 1: 6x-10=1; step 2: 6x=11