A drive sprocket has 15 teeth, and the driven sprocket has 60 teeth. If the driven sprocket must be replaced with a 48-tooth sprocket, how many teeth should be on the drive sprocket for the same speed?

To maintain the same speed when changing sprockets, it is important to understand the relationship between the number of teeth on the drive sprocket and the driven sprocket. The speed ratio between the drive and driven sprockets is determined by the number of teeth on each.

Initially, with a 15-tooth drive sprocket and a 60-tooth driven sprocket, the speed ratio can be calculated as:

Speed Ratio = (Number of teeth on driven sprocket) / (Number of teeth on drive sprocket) = 60 / 15 = 4.

This means that for every full turn of the drive sprocket, the driven sprocket turns a quarter of a turn, indicating it moves slower due to its larger size.

When replacing the driven sprocket with a 48-tooth sprocket, we want to find the number of teeth needed on the drive sprocket to keep the speed ratio the same. Thus, the new speed ratio must also equal 4. Therefore, we set up the equation:

Number of teeth on the new driven sprocket / Number of teeth on the new drive sprocket = 4.

Using the new driven sprocket:

48 / Number of teeth on new drive sprocket = 4