A gear with 20 teeth revolving at 200 revolutions per minute is meshed with a second gear turning at 250 revolutions per minute. How many teeth does this gear have ?

Well, the first gear is like a party animal, having 20 teeth and spinning at 200 revolutions per minute. The second gear, on the other hand, is trying to keep up, spinning at 250 revolutions per minute. So, let's calculate how many teeth it needs to have to maintain the rhythm.

To find the number of teeth on the second gear, we can use the gear ratio formula: Gear Ratio = (Number of Teeth in Second Gear) / (Number of Teeth in First Gear).

Now, we know that the gear ratio is 250/200, which simplifies to 5/4. To maintain this ratio, the second gear needs to have 5/4 times the number of teeth as the first gear. Since the first gear has 20 teeth, the second gear should have 5/4 * 20 = 25 teeth.

So, the second gear should have 25 teeth to keep up with the first gear's wild dance moves.

To find out the number of teeth on the second gear, you can use the concept of the gear ratio.

The gear ratio is defined as the ratio of the number of teeth on the driving gear to the number of teeth on the driven gear. In this case, the first gear is the driving gear with 20 teeth, and the second gear is the driven gear.

The gear ratio can also be calculated using the formula:

Gear Ratio = (Number of Teeth on Driven Gear) / (Number of Teeth on Driving Gear)

Using the given information, we have:

Gear Ratio = (250 revolutions per minute) / (200 revolutions per minute) = 1.25

Since the gear ratio is equal to the ratio of the number of teeth, we can set up the equation:

1.25 = (Number of Teeth on Driven Gear) / 20

Now, we can solve for the number of teeth on the second gear:

(Number of Teeth on Driven Gear) = 1.25 * 20 = 25

Therefore, the second gear has 25 teeth.

since the total number of teeth/min must match,

20*200 = n*250

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