Word Problem about finding time and rate

Question

To travel 75 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen to travel 40 miles riding a bicycle. Sue travels 17 miles per hour faster than Doreen. Find the times and rates of both girls.

Answer 1

 

 75 = (T-2)*R = RT - 2R

 

 40 = T * (R-17) = RT - 17T

 

35 = 17T - 2R

 

(35 + 2R)/17 = T

 

40 = (35+2R)/17 * (R-17)

 

680 = (35+2R)(R-17)

 

680 = 35R - 595 + 2R^2 - 34R

 

680 = R - 595 + 2R^2

 

 2r^2 + r - 1275 = 0

 

(  2r    +   51 )(r  -       25  ) = 0

 

 

2r+51 results in negative measures

 

r-25=0 ---> r = 25

 

 

25*3 = 75

 

8 * 5  = 40