To travel 96 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 63 miles riding a bicycle. Sue travels 15 miles per hour fast

Question

idk how to solve the equation

Answer 1

distance = rate x time

 

Doreen speed on the bike is r.

Dorren time on the bike is t.

 

96 = (r+15)*(t-3) <-- 15 mph faster and 3 hours less time

 

63 = r * t = rt

 

FOILs the top equation:

96 = rt - 3r + 15t - 45

 

141 = rt - 3r + 15t

 

141 = 63 - 3r + 15t

 

78 = -3r + 15t

 

78 = 15t - 3r

 

26 = 5t - r

 

r + 26 = 5t

 

(r + 26)/5 = t

 

rt = r(r+26)/5 = 63

 

r^2 +26r = 315

 

r^2 + 26r - 315 = 0

 

(r    +   35)( r   -  9  ) = 0

 

r + 35 = 0 ----> r = -35; disqualified/rejected, as rate of speed cannot be negative

 

r-9 = 0 ---> r = 9

 

Dorren rides the bike at 9 mph, for 63/9 = 7 hours.

 

Sue rides the moped at 24 mph, for 94/24 = 4 hours, which is 3 hours less time.