Question is incomplete :
The speed, S, of a bicycle varies directly with the number of revolutions per minute, R, that the pedals turn and the number of teeth on the front gear, F, and inversely with the number of teeth on the back gear B.
Lars is racing at 24 miles per hour. His front gear has 52 teeth and a back gear has 14 teeth. He is pedaling 84 revolutions per minute. As he sprints for the finish line, he pedals 112 revolutions per minute. What is his speed?
Answer:
32 mph
Step-by-step explanation:
Speed α number of revolutions α number of teeth on front gear α 1/teeth on back gear
Speed = S ; number of revolutions = R ; Number of teeth on front gear = F ; Number of teeth in back gear = B
S = k(R * F) / B
k = proportionality constant ;
24 = k(84 * 52) / 14
24 * 14 = 4368k
k = 336/4368
k = 0.0769230
Speed at R = 112
S = k(R * F) / B
S = 0.0769230(112 * 52) / 14
S = 447.999552 / 14
S = 31.999968
S = 32 mph
