When two gears are mashed the revolution per minutes (rpm) are inversely proportional to the number of teeth, as show below. In one machine the rpm ratio of the larger gear to the small gear is 4:7 The small gear has 216 teeth In second machine the larger gear revolves at 400 rpm and has 315 teeth. The smaller gear revolves at 700 rpm.
Find the number of teeth on the larger gear of the first machine?
Find the number of teeth on the small gear of the first machine?
To solve this problem, we can use the principle of inverse proportionality between the number of teeth and the RPMs of the gears.
Let's start with the first machine. We are given that the RPM ratio of the larger gear to the smaller gear is 4:7. We also know that the smaller gear has 216 teeth.
To find the number of teeth on the larger gear, we can set up a proportion using the RPM ratio:
(RPM of larger gear) / (RPM of smaller gear) = (number of teeth on smaller gear) / (number of teeth on larger gear)
Plugging in the given values, we get:
4/7 = 216/x
To solve for x, we can cross-multiply and solve for x:
4x = 7 * 216
x = (7 * 216) / 4
x = 378
Therefore, the number of teeth on the larger gear of the first machine is 378.
To find the number of teeth on the smaller gear of the first machine, we can simply use the given value of 216 teeth.
Now let's move on to the second machine. We are given that the larger gear has 315 teeth and revolves at 400 RPM, while the smaller gear revolves at 700 RPM.
Using the same principle of inverse proportionality, we can set up a proportion:
(RPM of larger gear) / (RPM of smaller gear) = (number of teeth on smaller gear) / (number of teeth on larger gear)
Plugging in the given values, we get:
400/700 = (number of teeth on smaller gear) / 315
To solve for the number of teeth on the smaller gear, we can cross-multiply and solve for it:
400 * 315 = 700 * (number of teeth on smaller gear)
(number of teeth on smaller gear) = (400 * 315) / 700
(number of teeth on smaller gear) = 180
Therefore, the number of teeth on the smaller gear of the second machine is 180.