Question 1154223
spent a total of 11 hours driving
parents who live 264 miles away
way there her average speed was 14 miles per hour faster than on her way home

Hi, 
D = rt  0r  t = D/r
WRITE AS YOU READ
 11 = 264/(r+14) + 264/r
Multiply each term by common Denominator..
11r(r+14)= 264r + 264(r+14) 
Simplify
r(r+14) = 24r + 24(r+14)   | DIVIDE EACH TERM BY 11
r^2 - 34r - 336  = 0       
(r + 8) (r  - 42 ) = 0     |336  factors 6*2*4*7  (8 & 42 works)
r = 42mph
Checking our Answer
264/56 + 264/42 = 11  0r
24/56 +  24/42 = 1
3/7 + 4/7 = 1  CHECKS!