Samantha can ride her bike to work in 2/3 of an hour. When she drives to work it takes 1/3 of an hour. If she drives 12 miles per hour faster than she rides her bike, how fast does she ride her bike?

Answer 1

D = RT (Distance = Rate x Time)
R = rate of bike
0.67 = time of bike (2/3 = 0.67)
0.67R = distance of bike

R + 12 = rate of car
0.33 = time of ca (1/3 = 0.33)
.33(R + 12) = distance of car

Since distance is equal
0.67R = 0.33(R + 12)

Solve for R, rate of bike