Rate is equal to distance per time. Going to the market, the equation is:
R = D/T
going back home, the rate is (¾)R, therefore the equation is:
(¾)R = D/(T + 12)
Since the distance is the same for both cases, equate the equations
RT = (3/4)R (T + 12)
T=(3/4)(T + 12)
(1/4)T = 9
T = 36
T+12 = 48
It takes Carmen 48 minutes to bike home.