When two gears are mashed, the revolutions per minute (rpm) are inversely proportional to the number of gears

Question

1. In one machine the rpm ratio of the large gear to the small gear is 2:3. The small gear has 94 teeth. In the second machine the large gear revolves at 300 rpm and has 360 teeth. The small gear revolves at 800 rpm. What is the number of teeth on the large gear of the first machine____. What is the number of teeth on the small gear of the second machine______.

                                    Rpm of large gear             # of teeth on small gear                   

                              ___________________=_________________________

                                    Rpm of small gear           # of teeth on large gear

 

Answer 1

R_L/R_S=T_S/T_L, so for 1st machine:

2/3=94/T_L, T_L=3(94/2)=3×47=141, the number of teeth on the large gear.

For 2nd machine:

300/800=T_S/360, T_S=360(300/800)=⅜×360=135, the number of teeth on the small gear.