Solve each problem.Selecting the Cogs Use the Formula from the previous exercise to answer...

Solve each problem.

Selecting the Cogs Use the Formula from the previous exercise to answer the following.

a. If a single-speed 27-in. bicycle has 17 teeth on the cog, then for what numbers of teeth on the chainring will the gear ratio be between 60 and 80?

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b. If a 26-in. bicycle has 40 teeth on the chainring, then for what numbers of teeth on the cog will the gear ratio be between 60 and 75?

Formula

Bicycle Gear Ratio The gear ratio r for a bicycle is defined by the formula

where N is the number of teeth on the chainring (by the pedal), n is the number of teeth on the cog (by the wheel), and w is the wheel diameter in inches.